unit plan - grade 11 u...
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Unit Plan - Grade 11 U Kinematics
OVERVIEW L LESSON TITLES (TOPICS/THEMES)
Kinematics is the branch of classical mechanics that describes the motion of objects
[1]. In this unit, students will explore the
physics of motion in one and two-dimensions. Students will
learn new concepts of scalars and vectors, differential properties of motion such as velocity and acceleration, as well as deriving
algebraic equations representing the relationship between the
different variables of motion.
Students will also explore the importance of kinematics in real-life applications. Students will spend 3 periods conducting
experimental work to strengthen their understanding of the new
concepts taught in this unit.
[1] Joseph Stiles Beggs (1983). Kinematics. Taylor & Francis.
p. 1
1 Distance, Position, and Displacement
2 Speed and Velocity
3 Acceleration
4 Comparing Graphs of Linear Motion
5 Five Key Equations for Motion with Uniform Acceleration
6 Acceleration Near Earth’s Surface
7 Experiment: Ticker Tape
8 Motion in Two Dimension
9 Projectile Motion – Day 1
10 Projectile Motion – Day 1
11 Experiment – Day 1: Projectile Motion Experiment
12 Experiment – Day 2: Projectile Motion Experiment & Write up
13 Motion in Our Lives
14
Unit Review
15 Unit Summative Assessment
OVERALL EXPECTATIONS L SPECIFIC EXPECTATIONS LEARNING GOALS
B1. Analyse technologies that apply
concepts related to kinematics, and
assess the technologies’ social and environmental impact;
B2. Investigate, in qualitative and quantitative terms, uniform and non-
uniform linear motion, and solve
related problems;
B3. Demonstrate an understanding of
uniform and non-uniform linear
motion, in one and two dimensions
1 B2.1, B3.2
Students will be able to:
Explain how distance, position, and displacement are different
Explain the difference between scalars and vectors
Calculate the displacement of an object algebraically and by a
vector scalar diagram
2 B2.1, B3.1, B3.2 Students will be able to:
Explain how speed and velocity are different
Explain the relationship between velocity, displacement, and
time
Determine velocity from position-time graph
3 B2.1, B3.1, B3.2 Students will be able to:
Explain the relationship between acceleration, velocity,
displacement, and time
Determine acceleration from velocity-time graph
Determine the difference between average velocity and
instantaneous velocity
4 B2.2, B3.1 Students will be able to:
Obtain information from position-time, velocity-time, and
acceleration-time graphs
Realize that given one type of motion graph, they can construct
a different type of graph
5 B1.1, B2.3, B2.4 Students will be able to:
Derive the 5 key equations of motion
Solve uniform velocity and uniform acceleration using algebraic
methods
6 B1.1, B2.6 Students will be able to:
Understand that the symbol of g is used to represent the
acceleration due to gravity Describe how the acceleration due to
gravity affects the motion of objects close to the surface of Earth
Describe how the acceleration due to gravity affects the motion
of objects close to the surface of Earth (g = 9.8 m/s2)
Understand the concept of terminal velocity
7 B1.1, B2.4, B2.6 Students will be able to:
Construct ticker tape experiment to explain the motion of a
moving car
Construct and obtain information from motion graphs
Present a scientifically written lab report
8 B2.5, B2.7 Students will be able to:
Describe how to determine total displacement in 2-deminsions
by scalar diagram and by component method
Solve problems that involve moving in 2-dimensions
9 B2.8, B3.3 Students will be able to:
Determine the factors affecting projectile motion (angle,
launching velocity, initial height, gravity, etc.)
10
B1.1, B2.8, B3.3 Students will be able to:
Understand that projectile motion consists of independent
horizontal and vertical motions
Understand that the horizontal and vertical motions take the
same amount of time
Understand that projectiles move horizontally at a constant
velocity, and undergo uniform acceleration vertically
Solve problems related to the horizontal and vertical
components of motion of a projectile using kinematic equations
(determine the range, maximum height, and time of flight foe a projectile’s motion)
11 B1.1, B2.9, B3.3 Students will be able to:
Use a projectile launcher to examine the properties of projectile
motion
Experiment the various factors that affect projectile motion
12 B1.1, B2.9, B3.3 Students will be able to:
Use a projectile launcher to examine the properties of projectile
motion
Experiment the various factors that affect projectile motion
Write a scientific lab report
13 B1.1, B1.2 Students will be able to:
Asses the social and environmental impacts of a technology that
applies kinematics concepts
14 B1.1, B2.1, B2.2, B2.3, B2.4,
B2.5, B2.6, B2.7, B2.8, B2.9,
B3.1, B3.2, B3.3
Students will be able to:
Determine the level of their understanding of kinematics
Ask for help if needed
15 B1.1, B2.1, B2.2, B2.3, B2.4,
B2.5, B2.6, B2.7, B2.8, B2.9, B3.1, B3.2, B3.3
Students will be:
At the expected level of understanding kinematics
Big Question L LITTLE BIG QUESTIONS LESSON OVERVIEW
How do we measure motion?
What are the applications of kinematics?
1 What is the difference between a scalar and a vector?
What is the difference between distance and
displacement?
Distance and displacement are two quantities that might seem the same, but actually have distinct meanings:
Distance: is a scalar quantity of how much ground did an
object cover
Displacement: is a vector quantity of how far out of place (original point) an object is
Scalar is only a measured magnitude
Vector is a measured magnitude + direction
2 What is the difference between speed and
velocity?
How to calculate speed and velocity?
Speed and Velocity are two quantities that might seem the
same, but actually have distinct meanings:
Speed: is the rate of change in distance ( v = d/t)
Velocity is the rate of change in displacement ( d t)
3 What is acceleration?
How to find acceleration from a velocity-time
graph
Acceleration is the rate of change in elocit a t)
Acceleration is the slope of a velocity-time graph
4 What is the relationship between displacement, velocity and acceleration from the graphs?
Velocity is the slope of displacement-time graph, and acceleration is the slope of the velocity-time graph. Velocity
is the area under the acceleration-time graph, and
displacement is the area under the velocity time graph
5 How to solve kinematic problems?
There are 5 equations in kinematics that will be derived. Each
equation has 3 known variables, one unknown variable, and one variable that is not used (there are five variables in total:
Δd, 1, v2, a, & t). Based on the given information from a
problem, students will know which equation to use.
6 What is a free fall?
How does an object in free fall behave when it
is close to earth surface?
What is terminal velocity?
When an object is in free-fall near the earth surface, it
accelerates downwards 9.8 m/s2 due to gravity. This value is
called “g”. In case of air resistance during free-fall, un object
will reach a point of constant speed called “terminal elocit ”
7 What are some of the applications of
kinematics?
Students will use a ticker tape timer to record the motion of
an accelerating toy car. They will create graphs of velocity
and acceleration versus time, and show how these graphs demonstrate constant acceleration.
8 How to calculate vectors in 2-dimenssion?
The understanding of the motion of objects in two
dimensions both conceptually and experimentally. When
completed the students should have an understanding of the vertical and horizontal components and how they relate to
each other. *
9 What is projectile motion?
What factors affect projectile motion?
Students will be introduced to projectile motion through
exploration with various ball-shaped objects. Factors that affect projectile motion will be discussed. **
10
How to analyze projectile motion in 2-
dimenssion?
Continuing discussion on projectile motion. Students will be
introduced to the river gorge supply delivery scenario and brainstorm ways to approach problems. Students will be
introduced to the next class’s experiment**
11 What are some of the applications of projectile
motion? At what initial degree would give the greatest
range?
This laboratory exercise is intended to allow students to
observe and vary the path of a projectile. Students will use a projectile launcher to test the trajectory path of the projectile
motion.
12 What are some of the applications of projectile
motion? At what initial degree would give the greatest
range?
Continuation of Day 11 + Lab report
13 What are real-life applications of kinematics? Students will explore real-life applications of kinematics. E.g.
automotive industry, missiles, free fall, etc.
14 How well prepared are you for the unit test?
Unit test review session. Students will be given sample questions to help them prepare for the unit test. Students may
work in groups. Few questions will be answered as class
discussion
15 How well will you do on the unit test?
Unit test
* www.bemidjistate.edu/academics/departments/science/k12-science-units/2D-motion-unit-HS-physics.pdf
** http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html
L HOTS MULTIPLE INTELLIGENCE
1 Knowledge, Comprehension Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
2 Knowledge, Comprehension Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
3 Knowledge, Comprehension Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
4 Knowledge, Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
5 Knowledge, Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
6 Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
7 Knowledge, Comprehension, Application, Analysis, Synthesis,
Evaluation
Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
8 Knowledge, Comprehension Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
9 Knowledge, Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
10 Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
11 Comprehension, Application, Analysis, Synthesis, Evaluation Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal,
Naturalistic
12 Comprehension, Application, Analysis, Synthesis, Evaluation Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal, Naturalistic
13 Comprehension, Application, Analysis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
14 Knowledge, Comprehension, Application, Analysis, Synthesis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
15 Knowledge, Comprehension, Application, Analysis, Synthesis Logical, Linguistic, Spatial, Kinesthetic, Interpersonal, Intrapersonal
L KEY RESOURCES (4) PRIOR KNOWLEDGE/LEARNING DIAGNOSTIC ASSESSMENT
1 Text book: Nelson Physics 11
Worksheet
Measurements and IS unites Class exercise (worksheet)
2 Text book: Nelson Physics 11
Worksheet
Scalar vs. vector Lesson review at the beginning of class
3 Text book: Nelson Physics 11
Worksheet
Displacement, velocity, rate of change Lesson review at the beginning of class
4 Text book: Nelson Physics 11
Worksheet
Graph paper
Relationships between displacement,
velocity, and acceleration
Worksheet
5 Text book: Nelson Physics 11 Worksheet
Chart paper
Relationships between displacement, velocity, and acceleration
Small group discussion. Represent relationships on a chart paper
6 Text book: Nelson Physics 11
Worksheet
Stopwatch, ticker tape timer, ticker tape, calculator, meter stick, ring stand support, pull-back car
Access to the computer lab
Acceleration and the rate of change of
velocity, gravity
Start class with a small demo involving free
fall. Ask students for their predictions
7 Text book: Nelson Physics 11
Worksheet Stopwatch, ticker tape timer, ticker tape, calculator,
meter stick, ring stand support, pull-back car
Kinematic equations
Writing a scientific lab report
Provide clear and thorough instructions
Ask student about key formulae Provide a brief lab demo
8 Text book: Nelson Physics 11 Worksheet
Graph paper, rulers
2-dimenssion, vectors and scalars, displacement
Lesson review at the beginning of class
9 Text book: Nelson Physics 11
Worksheet Various ball-shaped objects: paper balls, balloon,
cotton balls, rubber balls, tennis balls, golf balls
Kinematic equations
2-dimenssion motion
Class discussion
10
Text book: Nelson Physics 11
Worksheet Projectile launcher and plastic balls
Measuring sticks, Carbon paper and white paper,
Sticky tape, C-clamp
Factors that affect projectile motion from
previous class
Small groups worksheet review
11 Text book: Nelson Physics 11 Worksheet
Projectile launcher and plastic balls
Measuring sticks, Carbon paper and white paper, Sticky tape, C-clamp
Projectile motion Provide clear and thorough instructions Ask student about key formulae
Provide a brief lab demo
12 Text book: Nelson Physics 11
Worksheet
Projectile launcher and plastic balls Measuring sticks, Carbon paper and white paper,
Sticky tape, C-clamp
Access to the computer lab
Projectile motion
Writing a scientific lab report
None
(Lab day)
13 Text book: Nelson Physics 11
Worksheet
Chart paper
Kinematics Lesson review at the beginning of class
14 Text book: Nelson Physics 11
Worksheet
Kinematics Class discussion of important concepts in
kinematics
15 Test Papers Kinematics None
(Summative assessment)
L THREE STAGES OF LESSON DEVELOPMENT
1 Review of IS unites and measuring techniques
Worksheet exercise
Some lecturing,
Class discussion and activities on the scalars & vectors, and distance & displacement
Class debriefing
2 Review of previous class
Discuss the concept of speed
Some lecturing,
Class discussion and activities on speed vs.
velocity. How are they calculated? Worksheet
Class debriefing
3 Review of previous class
Ask class what if an object doesn’t mo e in a constant velocity?
Some lecturing,
Class discussion and activities on acceleration. How is it calculated? Worksheet
Class debriefing
4 Review of previous class (worksheet)
Class discussion and activities on the relationships between displacement, velocity,
and acceleration-time graphs
Working on worksheet and graphs
5 Review of previous. Small group discussion.
Represent relationships on a chart paper
Give a simple kinematics problem.
Derivation of the 5 kinematics question Work on an inquiry-based problem
6 Start class with a small demo involving free fall. Ask students for their predictions
Some lecturing, Class discussion and activities on free fall.
How about free fall in other planets?
Work on worksheet Introduction to next class lab experiment
7 Provide clear and thorough instructions
Ask student about key formulae
Provide a brief lab demo
Help students with their experiment and lab report
8 Review of scalars and vectors in 1-D Some lecturing,
Class discussion and activities on calculating vectors in 2-D. Worksheet
Class debriefing
9 Ask students if they know anything about projectile motion?
Discuss applications of projectile motion
Some lecturing, Class discussion and activities on factors
affecting projectile motion
Class debriefing
10 Groups of 4 worksheet review Inquiry-based problem on projectile motion Class debriefing
Introduction to next class lab experiment
11
Provide clear and thorough instructions
Ask student about key formulae Provide a brief lab demo
Help students with their experiment
12 Ask students to spend 5 minutes reviewing what they have done so far from the previous
day and what needs to be done for this lab
Help students with their experiment Help students with their lab report
13 Overall review and ideas of kinematics
applications
Students form groups of 4. Each group has to
come up with a written paragraph on one
application of kinematics. They have to use scientific knowledge learnt
5-minutes presentation/group on kinematics
applications
14 Class discussion of important concepts in
kinematics
Students work on the review sheet Answering few questions on the board
15 Unit Test
L FORMATIVE ASSESSMENT SUMMATIVE ASSESSMENT
1 Class performance and group work None
2 Class performance and group work None
3 Class performance and group work None
4 Class performance and group work Hand in worksheet and descriptions on displacement-time, velocity-time, and acceleration-time graphs. The relationships between these
graphs
5 Inquiry-based problem based on kinematics equations Students submit their solution
6 Class discussion and debriefing None
7 Performance during experiment Final lab report
8 Class performance and group work None
9 Class discussion and debriefing None
10 Inquiry-based problem based on projectile motion Students submit their solution
11 Performance during experiment None
12 Performance during experiment Final lab report
13 Group discussion 5 minutes presentation on applications of kinematics
14 Solving some practice problems on the board None
15 None Summative test
Lesson Plan – Day 9
Title: Intro to projectile motion Subject: Grade 11 Physics Time: 11:00 – 12:15 Strand: Kinematics
Desired Results
Lesson Description
This is the first lesson on Projectile motion. Students will be introduced to projectile motion through exploration with various ball-shaped objects. Factors that affect projectile motion will be discussed.
Ontario Curricular Overall Expectations
B2. investigate, in qualitative and quantitative terms, uniform and non-uniform linear motion, and solve related problems;
B3. demonstrate an understanding of uniform and non-uniform linear motion, in one and two dimensions
Ontario Curricular Specific Expectations
B2.8 use kinematic equations to solve problems related to the horizontal and vertical components of the motion of a projectile
B3.3 describe the characteristics and gi e examples of a projectile’s motion in ertical and horizontal planes
Lesson Goals
- Students develop an appreciation of projectile motion through various methods, and investigate what variables affect the flight path
(various objects, angles ,initial speed, mass, diameter, initial height, with and without air resistance)
- Use reasoning to explain the predictions.
Success Criteria
- Use reasoning to explain the predictions
- Explain common projectile motion terms in their own words
Assessment
Assessment Mode: Teacher and class provide feedback on the ideas that are generated
Materials
Various ball-shaped objects: paper balls, balloon, cotton balls, rubber balls, tennis balls, golf balls
Worksheet
Lesson Format : What Teachers Do/Say This lesson plan was inspired from: http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html
Real Time Activities Time
11:00 Introduction
- Draw a trajectory of a projectile motion on the board and ask student if they know anything that
moves in that motion.
- Explore some of projectile motion applications with the students. E.g. Soldiers and weapon,
firefighters, food packets thrown from helicopters
10
11:10 Exploration
- Students will be split into groups of 3 and will be given at least two different types of balls. Each
group should come to consensus on the factors that affect the shape and duration of the flight path of
the balls.
- Teacher should monitor groups, asking guiding questions to encourage brainstorming
30
11:40 Class Discussion
- Lead class discussion of what factors affect projectile motion. Allow different teams to defend their
choices and come to a class consensus on the important factors. Fill out the worksheet.
30
Lesson Reflection: Teacher and Lesson
To be filled after class
Lesson Plan – Day 10
Title: Projectile motion: Inquiry-based problem Subject: Grade 11 Physics Time: 11:00 – 12:15 Strand: Kinematics
Desired Results
Lesson Description
This is the Second lesson on Projectile motion. Students will explore the applications projectile motion through an inquiry-based problem.
Ontario Curricular Overall Expectations
B1. analyse technologies that apply concepts related to kinematics, and assess the technologies’ social and en ironmental impact;
B2. investigate, in qualitative and quantitative terms, uniform and non-uniform linear motion, and solve related problems;
B3. demonstrate an understanding of uniform and non-uniform linear motion, in one and two dimensions
Ontario Curricular Specific Expectations
B1.1 analyse, on the basis of research, a technology that applies concepts related to kinematics
B2.8 use kinematic equations to solve problems related to the horizontal and vertical components of the motion of a projectile
B3.3 describe the characteristics and gi e examples of a projectile’s motion in ertical and horizontal planes
Lesson Goals
- Understand that projectile motion consists of independent horizontal and vertical motions
- Understand that the horizontal and vertical motions take the same amount of time
- Understand that projectiles move horizontally at a constant velocity, and undergo uniform acceleration vertically
- Solve problems related to the horizontal and vertical components of motion of a projectile using kinematic equations (determine the
range, maximum height, and time of flight foe a projectile’s motion)
Success Criteria
- Be able to solve inquiry-based projectile motion problems
Assessment
Assessment Mode: Teacher and class provide feedback on the ideas that are generated.
Teacher will collect students; solution of the problem for marks
Materials
“Projectile Motion Unit Pre-test” worksheet
“Ri er Gorge Scenario” worksheet
Projectile motion lab handout
Projectile launcher and plastic balls
Measuring sticks
Carbon paper and white paper
Sticky tape
C-clamp
Lesson Format : What Teachers Do/Say This lesson plan was inspired from: http://www.ncsec.org/cadre2/team29_2/catapult/Lesson_Plans__Projectile_Motion_to_the_Rescue.html
Real Time Activities Time
11:00 Introduction
- Ask students to form groups of 4
- Had out the worksheet (see attachment: Projectile Motion Unit Pre-test) and ask groups to work on it
- Discuss the worksheet with the class
20
11:20 Exploration
- Introduce scenario to students and brainstorm ways to approach the River Gorge supply delivery (see 40
attachment).
- Students may work on the problem alone or groups of two.
- Collect students’ work at the end of the work session.
12:00 Conclusion: introducing next class experiment – Teacher’s Demo
- Teacher uses Projectile launcher and plastic balls (and other materials listed) to introduce students to
the experiment they will explore next class
- Distribute lab handout to give students a head start of what to expect
10
Lesson Reflection: Teacher and Lesson
To be filled after class
Projectile Motion Unit Pre-test
This activity is meant to test your prior knowledge going into our chapter on projectile motion. Please do the best that you can, but do not be
discouraged if you don’t know the answers! You will not be graded on this activity. Based on the class’ answers, we will tailor our learning to
ensure everyone will be challenged but not overwhelmed.
1) What force causes an object to fall to the ground when dropped?
Gravity
2) Does a ball dropped out of the window of a moving car take longer to reach the ground than one dropped at the same height from a car at
rest? Why or why not?
No, both balls reach the ground at the same time. This is because motion in the horizontal and vertical directions are independent of one another.
Thus, the fact that the ball dropped from the moving car has a horizontal velocity does not affect the amount of time it take for it to hit the ground.
3) Does the angle of take-off matter to a long jumper? Why?
Yes, the angle will affect how far the long jumper will travel. Using our equation for displacement in the x-direction we see that the distance
depends on the cosine of the launch angle.
4) What is velocity?
Velocity is equal to the change in distance divided by the change in time.
5) Can you find the cosine of 80°?
Cos(80 degrees)=0.7648
6) A soccer ball is kicked at an angle of 20 degrees at 15 m/s and lands 2.5 s later. Determine the distance the ball travels along the ground.
Given: Angle (θ) 20 degrees
Initial Velocity (vi) =15 m/s
Time of Flight (t) =2.5 s
Find: distance traveled in x-direction
Equation: Δx i*cos θ)*t
Δx 36.96 m or 37 m
River Gorge Scenario
You are 6 days into a 2 week hiking trip with a group of friends near the Royal Gorge in Colorado. As you walk along the trail you notice
how steep the cliff walls are that drop down into the Gorge. You and your friends are trying to decide how deep the gorge is (about 365 m)
when you hear cries for help coming from across the Gorge. You notice a group of hikers who appear to be stranded across the river.
They decided to cross the Gorge on a rickety old bridge that gave way just as their last group member finished crossing. The hikers indicate
to you that they have been stranded for 4 days now without any food or water. They are dehydrated and weak; you must do something to
help them! You all try your cell phones but you have no signal. Two of your group members volunteer to hike back out of the wilderness to
alert the authorities, but you know that you must do something to help the hikers until someone can come rescue them. But how will you get
food and water across the Gorge to them? The cliff walls are too steep to climb down. Can you think of any way to help them?
UNIT TEST Taken from: http://webcache.googleusercontent.com/search?q=cache:MfG-lQdvAbYJ:pplazekgrade11physics.wikispaces.com/file/view/SPH3U%2B-
%2BKinematics%2BUnit%2BTest%2Bwith%2Bsolutions.docx+&cd=1&hl=en&ct=clnk&gl=ca
COURSE: PHYSICS, GRADE 11 COURSE CODE: SPH3U
University Preparation
UNIT : KINEMATICS Maximum Marks: 50
Time allotted: 75 minutes
General Instructions:
All Questions are compulsory.
Question No. 1 contains 7 multiple choice questions of 1 mark each.
Question No. 2 contains 5 True-False type questions of 1 mark each.
Question No. 3 to 6 are short answer questions of 2 marks each.
Question No. 7 & 8 are problem solving questions of 10 marks each.
Question No. 9 is long answer question of 10 marks.
Q 1 Following are the multiple choice questions. Tick out the correct answer. (K/U)
1. The term “uniform motion” means a. acceleration is constant d. displacement is constant b. speed is constant e. velocity is zero c. velocity is constant
2. The area under a velocity-time graph always represents a. Displacement d. acceleration b. change in velocity e. change in acceleration c. distance
3. The position time graph pictured below represents the motions of two objects, A and B. Which of the following statements concerning the objects’ motion is true?
a. Object B travels the greater distance
b. Object A has the greater speed
c. Object A leaves the reference point at the earlier time
d. Both of the objects have the same speed at the point where the lines cross.
e. Object A is travelling for a longer period of time
4. The distance travelled by a body is directly proportional to the square of the time taken. It’s acceleration
a. Increases c. becomes zero
b. Decreases d. remains constant
5. A ball is thrown vertically into the air and when it returns after an interval of 2 seconds, it is caught. Which one of the following statements is true if the acceleration due to gravity is 10 m/s2 and air resistance can be neglected: a. The acceleration at the top of its flight is 10 m/s2. b. The time taken for the descending motion does not equal the time taken for the ascending motion. c. The maximum height it reaches does not depend on the force of gravity. d. The acceleration after it leaves the hand is 10 m/s2 downwards.
d
A
B
t
Position vs Time
6. A rock is thrown vertically upwards with a speed 'v' from the edge of a cliff. At the same moment, a second rock is thrown vertically downwards with the same initial speed 'v'. Which of the following statements regarding the motion of the rocks is true (ignore air resistance.)? a) The rock which was thrown upwards reaches the bottom of the cliff with a higher velocity. b) The rock which was thrown downwards reaches the bottom of the cliff with a higher velocity. c) Both rocks reach the bottom of the cliff with the same velocity at the same time. d) Both rocks reach the bottom of the cliff with the same velocity but at different times.
7.
The path PQR of a soccer ball kicked
from a point P on the ground is shown
in the diagram at the right. At point Q,
the ball is at its maximum height.
Which ONE of the following vectors may represent the acceleration due to gravity of the ball at point Q?
a) A b) B
c) C d) D
Q 2. State TRUE or FALSE for the following statements: (K/U & C)
1. A very massive object will free fall at the same rate of acceleration as a less massive object.
2. An object which is slowing down is represented by a line on a velocity-time graph which is moving in the downward direction.
3. An object with a positive acceleration will be represented on a position-time graph by a line which curves upwards.
4. The direction of the acceleration vector is dependent upon two factors: the direction the object is moving and whether the object is speeding up or slowing down.
5. Person X moves from location A to location B in 5 seconds. Person Y moves between the same two locations in 10 seconds. Person Y is moving with twice the speed as person X.
Q 3. A train of 150m length is going towards north direction at a speed of 10 m/s. A parrot flies at a speed of 5m/s towards south direction parallel to the
railway track, find the time taken by the parrot to cross the train? (K/U)
Q 4. The direction in which an object moves is given by the direction of velocity of the object and not by the direction of acceleration. Explain the
statement with suitable example. (A & C)
Q 5. In long jump, does it matter how high you jump? What factors determine the span of the jump?
(K/U & C)
Q 6. There are two displacement vectors, one of magnitude 3 meters and the other of 4 meters, how would the two vectors be added so that the
magnitude of the resultant vector be (a) 7 meters (b) 1 meters? (K/U)
Q 7. A shell was fired from ground level with an initial speed of 3.5 x 102 m/s at an angle of 30o to the horizontal. Estimate:
(K/U)
i its time of flight;
ii its maximum altitude
iii its range
Q 8. Two sport cars start from rest at the same place. One accelerates at 0.90 ms-2 for 15 s, and continues at constant speed there after. The other accelerates at 0.85 ms-2 for 20 s and then remains at that speed. Draw both journeys on the same velocity-time graph and determine the time and distance that the second car overtakes the first car. (K/U)
Q 9. When a skydiver jumps from an airplane she can reach speeds near 140 km/h during the freefall portion of the dive. Once the parachute is
deployed the parachutist’s speed decreases to 10 km/h. Explain why then in physics we consider the acceleration during the freefall to be
negative and the acceleration during the time the parachute is deployed to be positive by using your knowledge of vectors and kinematics. (A)
SOLUTIONS
Q 1. 1. c
2. a
3. b
4. d
5. d
6. d
7. c
Q 2. 1. True
2. False
3. False
4. True
5. False
Q 3. Relative velocity of Parrot with respect to train = 5+10 = 15m/s
Time taken by parrot to cross the train, t = 150/15 = 10s
Q 4. When an object is thrown up, the direction of motion of the object and hence its velocity is along vertical in upward direction. As the object moves
up, it is always attracted by earth in downward direction i.e., the acceleration is in vertical downward direction. Hence the direction of motion of the
object is that of velocity and not that of acceleration.
Q 5. Yes, in long jump, it matters how high one jumps, it is explained below.
For initial velocity u and angle of projection ϴ the maximum height,
h = u2 Sin2ϴ or u2 = 2 h
2g g Sin2ϴ
and, horizontal range, R = u2 Sin 2 ϴ = 2 h 2Sin ϴ Cos ϴ = 4h Cot ϴ
g Sin2ϴ
Thus the span of jump depends upon (i) height h attained (ii) angle of projection, ϴ.
Q 6. The magnitude of resultant R of two vectors A and B is given by
R = √ A2+B2+ 2 AB Cos ϴ ; where A=3m and B=4m
Now R = √ 32+42+ 2×3×4 Cos ϴ .
(i) R will be 7m if ϴ = 0o
(ii) R will be 1m if ϴ = 180o
Q 7. Take up as positive.
Initial horizontal speed = 3.5 x 102 m/s cos 30o
= 3.0 x 102 m/s
Initial vertical speed = 3.5 x 102 m/s sin 30o
= 175 m/s
Vertical Motion to top of flight:
v1 = +175 m/s
v2 = 0
a = -9.81 m/s2
t = [v2 - v1]/t = 17.8 s
So, time of flight = 2 x 17.8 s = 36 s
vav = [175 m/s + 0]/2 = 87.5 m/s
So, y = vav t = 87.5 m/s x 17.8 s = 1.6 x 103 m
Horizontal Motion:
x = vx t = 3.0 x 102 m/s x 36 s = 1.1 x 104 m
Q 8.
The velocities they reach are 0.9 × 15 = 13.5 ms-1 and 0.85 × 20 = 17 ms-1 respectively. Similar to the problem above, we have: First car (red) distance at time t = 1/2 × 13.5 (t + t - 15) Second car (blue) distance at time t = 1/2 × 17 (t + t - 20) The distance when they meet is the same, so: 1/2 × 13.5 × (2t - 15) = 1/2 × 17 × (2t - 20) Solving gives: Time = 19.643 s
Distance = 163.93 m
Q 9. Since the skydiver jumps from a plane the acceleration due to gravity causes the divers speed to increase in the negative direction. Therefore the
diver’s velocity continues to become more negative over time. If the diver is traveling at a speed of 140km/h, his/her velocity would be -140km/h or
140km/h [D]. Once he/she pulls deploys the parachute, the speed begins to decrease meaning that the velocity is becoming less negative. i.e. changing
from -140km/h to -10km/h. Therefore from a vector perspective the change in velocity is positive
∆v = v2 – v1
= (-10) – (-140) = +130 m/s
Since the velocity changes positive, therefore the acceleration must be positive.
i.e. a = ∆ v / ∆ t