linear motion speed velocity acceleration displacement time to draw the line time

Linear Motion

Speed

Velocity

Acceleration

Displacement

Time To Draw The Line

Time

The basic parameters in kinematics are time, distance, speed, and acceleration

Kinematics

Kinematics is a branch of mechanics.

Kinematics - The science of describing the motion of objects using words, diagrams, numbers, graphs, and equations.

1

The Greek letter Delta is used in mathematics and physics formulas as the symbol for "change in“

For example

The Greek Letter Delta

V Would symbolize a changein the velocity of an object.

2

A rate is any change that takes placeover time.

For example, your rate of growth is howmuch your height changes over a certain period of time.

Changes in the motion of objects thattake place over time intervals are veryimportant concepts in Physics.

3

Magnitude: A number assigned to a quantity sothat it may be compared with other quantities.

Example:The magnitude (size) of the diameter of the large circle is three. The magnitude of the diameter of the small circle is 1.

4

Seismologists use a Magnitude scale (called the Richter Scale) to express the seismic energy released by each earthquake.

Other Examples of magnitude

1. In February 2010, Chile was hit with a destructive earthquake with an 8.8-magnitude (size) on the Richter Scale.

2. Astronomers assign a magnitude (number) to indicate how bright a star appears in the sky. The star Vega has an apparent magnitude of 0.03.

The mathematical quantities which are used to describe the motion of objects can be divided into two categories:

Vectors are quantities which are fully described by both a magnitude and a direction. Vectors are usually represented by arrows. 5, 6

Scalars are quantities which are fully described by a magnitude (or numerical value) alone.

A 5 m

B 30 m/sec, East

C 5 mi., North

D 20 degrees Celsius

E 256 bytes

F 4000 Calories

Categorize each quantity as being either a vector or a scalar.

Scalar – magnitude but no direction

Scalar – magnitude but no direction

Scalar – magnitude but no direction

Scalar – magnitude but no direction

Vector – both magnitude and direction

Vector – both magnitude and direction

7

Remember:

A scalar quantity has only magnitude.

A vector quantity has both magnitude and direction

Scalar Quantities

Length MassArea DensityVolume PressureSpeed EnergyPower Distance

Vector Quantities

Displacement

DirectionVelocity AccelerationMomentum ForceWeight DragLift Thrust8, 9

Position is a location.

It’s where somethingis in the world.

Distance is a scalar quantity which refers to how far an object has moved or changed position.

10

The dot on the left is the initial position and the dot on the right is the final position.

The change in position from one place to another is distance.

Displacement refers to an object's overall change in position.

Displacement is a vector quantity.

Displacement is not always equal to the distance traveled.

The unit for distance and displacement is meters.

11, 12, 13, 14

A physics teacher walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North.

Even though the physics teacher has walked a total distance of 12 meters, her displacement is 0 meters.

Distance vs. Displacement• You drive the path, and your odometer

goes up by 8 miles (your distance).

• Your displacement is the shorter directed distance from start to stop (yellow arrow).

start

stop

What if you drove in a circle?

Formula for calculating displacement:

x = the displacementXf = the ending position Xi = the starting position

Ignore the path of the object. All you need are the fixed endpoints.

To find displacement determine the shortest distance between the starting position and ending position of the object.

How to Solve for Displacement in Physics

15, 16, 17

Relative Motion AndReference Point

Motion occurs when an object changes position.

The change in the position of one body relative toanother is the concept of relative motion.

To know whether the position of an object haschanged, you need a reference point such as themailbox below.

18, 19

All motion is relative to the observer or to some fixed object.

Jack and Jill sitting in a room.  Jill sees Jack at rest and Jack sees Jill the same way. 

It is only when we "zoom out" on our point of view that we discover that Jack and Jill are on a bus moving with a constant velocity (same amount and direction). 

Jack and Jill are looking at each other from the reference frame of the bus.

Jill's Mother, waiting for her own bus, sees Jill's bus go by at 25mph.  She sees Jill traveling 25mph.  Jack on the other hand, sees Jill going zero mph.  What they observe seems to depend on their state of motion (frame of reference).

Speed

Speed: the rate at which an object changes position (or the distance an object travels per unit of time).

Speed is a scalar quantity

Formula for calculating speed:

Speed = distance / time (s = d/t)

SI unit for speed: Meters per second (m/s)

Any combination of distance and time units can be used to describe speed, such as

kilometers per hour (km/hr)centimeters per second (cm/s)

20, 21, 22, 23

Most of the time, the speeds you experience are changing.

Average Speed describes the motion of an object when its speed is changing.

How would you express your speed on a trip where you speed varies?

Physics classroom 24

Average speed formula

The total distance traveled divided by the total time traveled.

Average speed = total distance/total time

Farmer Jones drives 6 miles down a straight road. She turns around and drives 4 miles back. What was her average speed for this trip if it took 1 hour?

Avg. speed = 10 miles / 1hour or 10 mphPhysics classroom 25

Average speed = total distance/total time

The girl in the picture covered the distance indicated by the blue arrows in 7 seconds.

What was her average speed?

Average speed = total distance/total time15 m / 7 sec = 2.1 m/s

What is the total distancetraveled by the girl?

15 meters

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The speed shown on this speedometer gives the instantaneous speed.

Instantaneous speed is the speed of an object at any given point in time.

Instantaneous Speed

26

Constant speed: When a moving object covers the same distance every regular interval of time.

Example:

A car is moving with a constant speed of 10 m/s in a straight line.

This means that the car is covering a distance of 10 meters every second.

27

Constant Speed

A constant speed graph shows a constant & positive slope

Physics classroom

Changing Speed

An object with a changing speed would be movinga different distance each second. Changing speed on a position time graph is acceleration.

Physics classroom

28, 29

Velocity

Velocity: the rate at which an object changes its position plus the direction of the change of position.

Velocity is speed + direction

Velocity is a vector quantity Velocity is not the same as speed.

Speed is a description of how fast an object moves.

Velocity is a description of how fast and in what direction an object moves.

30, 31, 32, 33

Can an object have a constant speed and also have a changing velocity? Yes

To change velocity an object can undergo a change in either

its speed its direction

or both

The speed of this car moving around a circulartrack might be constant, but its velocity is notconstant because at every point on the circle,the direction of motion is always changing.

34

The weatherman will report a hurricane's velocity as 20 kilometers per hour moving in a northwesterly direction.

People want to know how fast a hurricane is traveling but they also need to know in what direction it is traveling.

Adapted from science Joy Wagon

A constant velocity means equal changesin displacement for each time interval.

35

Adapted from Science Joy Wagon

Average Velocity

Average velocity is an object’s totaldisplacement divided by the time intervalduring which the displacement occurred.

The SI unit for velocity is m/s

final displacement

total time takenAverage velocity =

36, 37, 38

12 m

displacement

A physics student walked a 30 meter path in 6 seconds.

What was the student’saverage speed?

What was the student’saverage velocity?

Avg. Speed = d/t30 m / 6 seconds =5 m/s.

Avg. velocity = displacement/time12 meters / 6 seconds =2 m/s

(in a direction that's approximately 110° from vertical). www.worsleyschool.net

Average velocity will always be zero when the final displacement is zero.

The girl covered the distance in 7 seconds.

Average velocity = displacement/time

0/7s = 0 m/s

Average velocity = Displacement/time

What is her displacement?

0 since she ended up backwhere she started.

What is the average velocityof the girl?

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A. Velocities with a direction to the East (right) or to the North (up) are positive.

B. Velocities with a direction of West (left) or South (down) are negative.

Velocity has direction and the direction can be represented in a coordinate plane.

39, 40,41

When two objects move in the same direction their velocities have the same sign.

42

If two objects are traveling in opposite directions, one object has a positive direction and the other has a negative direction.

43

Acceleration

AccelerationUsain Bolt won the 100 yard dash in the ’08 Summer Olympics by .02 of a second, the largest margin of victory in 40 years.

Two hundredths of a second might not seem like much but the picture above proves otherwise.

Whenever a velocity is not constant, we say it is accelerating.

An acceleration means differing changes indisplacement for each time interval.

Adapted from Science Joy Wagon

Acceleration: The rate at which an object changes its velocity. (how fast velocity changes).

Acceleration is a vector quantity

Which car or cars (red, green, and/or blue) are undergoing an acceleration?

Physics classroom 44, 45

We say an object is accelerating if:

A. It’s velocity is increasing.

Adapted from Science Joy Wagon 46 A

We say an object is accelerating if:

B. Its velocity is decreasing. Decreasing velocity is still acceleration, although it is negative acceleration.

Adapted from Science Joy Wagon46 B

We say an object is accelerating if:

C. Its direction is changing, which means that velocity is changing even if speed stays the same.

Adapted from Science Joy Wagon

46 C

Where:

1.vf - final velocity

2.vi - initial velocity

3. t - time

Formula for Calculating Acceleration

Adapted from Science Joy Wagon

47 A, 47 B

Meters per second per second

Read as:

Meters per second squared

Units for Acceleration

Adapted from Science Joy Wagon

48

A large acceleration tells you that velocity is changing quickly.

A small acceleration tells you that velocity is changing slowly.

An acceleration of zerotells you that velocityis not changing.

49 A, 49 B, 49 C

In physics, acceleration is not just an increase in velocity, but also a decrease in velocity.

A decrease in velocity is a negative acceleration.

This actually helps when doing calculations and also allows us to give more meaning to acceleration.

50

You are walking down the street when you see an enormous, 112kg barrel rolling towards you at 12 m/s.

You are, of course, surprised by a barrel of this size, let alone the fact that it is rolling down the street. You jump in front of it and begin pushing on it until you finally bring it to a stop 27.4s later.

At this point you are arrested for interfering in the “World’s Largest Barrel Rolling Championships”.

Determine the acceleration of the barrel.

In this example you have a barrel that is initially moving and ends up at rest.

a = Δv / Δt =(vf - vi) / t

= (0 - 12) / 27.4

a = -0.44 m/s2

Notice that a final velocity of zero (you stopped it), minus another number gives you a negative Δv.

A positive velocity means an object is going in the positive direction (like forwards), and a negative direction is backwards.

A negative acceleration can mean…

1. An object moving in the positive direction (positive velocity) is slowing down.

Or

2. An object moving in the negative direction (negative velocity) is speeding up.

51 A, 51 B

Direction Speeding up

Slowing

Down

Right + + (+ x +) +

Right + - (+ x -) _

Left - - (- x -) +

Left - + (- x +) _

Acceleration

Note: a negative acceleration does not always mean the object is slowing down.

52

Examples of acceleration

A rocket powered dragstergoing from 0 to 300 mphin 3 seconds!!!

A dragster slamming into a concrete barrier!

positive

negative

You drop something off a cliff.As it falls, gravitycauses it to accelerate.

positive

negative

Throw a ball up in the air. As it rises, gravity causesa negative acceleration in the direction the ball wastraveling, causing the ball toslow down, stop, and begin todescend.

Examples of acceleration

1 sec after moving its going 2 miles an hour. 2 sec after moving its going 4 miles an hour. 3 sec after moving its going 6 miles an hour.4 sec after moving its going 8 miles an hour.

Constant Acceleration: When an accelerating object changes its velocity by the same amount each second.

53

The velocity-time graph for constant acceleration is a straight line.

What would the velocity of the object be after 6 seconds?

54

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