Unit 2 Study Guide: Uniform Linear Motion Name: KEY

Due: SEPTEMBER 30 (TEST DAY)

Variable

Vocabulary word

S.I. unit

Equation

Definition

d

distance

Meters, m

d = st or

the sum of the lengths of all legs of a journey

The length of the path traveled; is a scalar

Displacement

‘Change in’ position

Meters, m

The change of position between start and end point along a linear path; is a vector

s

speed

Meters/second

m/s

The rate at which distance is covered; is a scalar

velocity

Meters/second

m/s

The rate of change of position over time; is a vector

t or Δt

time

seconds

_______

Δt - The duration of an event

t - the clock reading when a particular event occurs

xi

Initial position

meters

_______

The location of an object at the beginning of an interval.

xf

Final position

meters

_______

The location of an object at the end of an interval.

Learning Target: I can analyze motion to find displacement and distance. BOP page 18 & 25

One dimensional motion (Side –to-side only)

1. What is the bee’s starting position? xi = -8.0 meters What is the bee’s ending position? xF = 0 meters

2. Does the bee change direction between the starting and ending point? Yes. Motion begins in the + direction then changes to the – direction.

3. Considering the bee’s motion from start to end, is the distance covered by the bee the same as the bee’s Δx? No.

4. To confirm your answer to number 3, calculate the distance and displacement of the bee from start to end:

Show all work. Include all variable names and formulas that may apply.

Distance Displacement

d = | Δx1 | + | Δx2 | = |20 m| + |-12m| = 32 m Δx = xf – xi = 0 m – (-8m) = + 8 m

Learning Target: I can calculate speed. BOP page 25

5. You are taking a road trip with your friends. To keep track of the distance that you drive, you start the trip calculator when you leave. When you return 5.4 hours later, the trip calculator shows that you have driven a distance of 264 miles. What was your average speed for the trip?

s = d/t = 264 miles / 5.4 hours = 48.9 miles/hour ( sig figs for this answer = 2 so s = 49 mph)

6. You ride your bike along a 64 mile section of the Katy trail. If you complete the 64 miles in 2.5 hours, find your average speed.

s = d/t = 64 miles / 2.5 hours = 25.6 miles/hour ( sig figs for this answer = 2 so s = 26 mph)

Learning Target: I can maximize the scale on the graph axis graph to help me identify trends in the data shown on the graph. BOP: page 13.

7. You need to graph the motion of a cart. You collected the data shown in the table below. Using the rules for scaling axis on page 13 of your BOP, scale the x and t axis appropriately. Add the appropriate units to the axis labels.

Learning Target: I can calculate the average velocity of an object from an x vs. t graph. BOP page ??

Learning Target: I can use time and position data to create graphs of motion. BOP page ???

8. Graph the motion of cars 2, 3, 4 5 and 7 on the previous page. See Graph.

9. Using the formula for Average velocity (BOP page ??) calculate the average velocities of all 7 cars.

The formula for average velocity is :

Average Velocity for Car 1:

Average Velocity for Car 2:

Average Velocity for Car 3:

Average Velocity for Car 4:

Average Velocity for Car 5:

Average Velocity for Car 6:

Average Velocity for Car 7:

10. Compare the cars with a negative velocity. How are the motions of those cars similar? All cars with (-) velocities move toward the (-) direction.

11. Compare the cars with a positive velocity. How are the motions of those cars similar? All cars with (+) velocities move toward the (+) direction.

12. At t = 1.5 seconds, compare the position of cars 1 and 6. At t = 1.5s, cars 1 and 6 are in the same location. Both cars are at approx. + 2.3 m.

13. Do cars 1 and 6 move in the same direction? Car 1 and car 6 move in opposite directions.

What happens at t = 1.5 seconds? See # 12 above.

Learning Target: I can describe an object’s motion based on the x vs. t graph. BOP page 22

direction, displacement, distance, starting position, starting time, ending position, ending time. BOP page ??

14. What is the starting position of the object whose motion is shown in the graph above? xi = 5 m

15. What direction is it travelling? It is travelling in the positive direction.

16. What is its position at t = 10 seconds? At t=10 seconds, the object’s position is 50 meters.

17. Use the graph to solve for the average velocity of the object.

Carefully read the right hand column of BOP page 23. Examine the graph along with the statement about the relative velocity and position of R and P.

18. Using what you have learned from this example. Create a graph below that meets the criteria listed.

Learning Target: I can use motion diagrams to model motion. BOP page 19 & 20

Review pages 19 and 20 of the BOP.

If you remember creating the ‘tape trail’ for the Battery Toy Car graph, you created a motion diagram from the positions on the tape.

19. What are the three elements of a motion diagram? ___________________ _______________________ ________________________

20. What is the minimum number of time intervals needed to establish a constant velocity interval from a motion diagram? 3

21. Examine the motion diagrams shown and complete the table. Assume that each element of the motion diagram represents one second. (one dot with a displacement vector represents one second).

Motion diagram

Initial position

Final

Position

Velocity

( + or - )

Time

Xi = 0 m

Xf =-13m

V =

-13m/6 s

=-2.16m/s

t =6s

Xi =-13 m

Xf = 0 m

V =

+13m/6 s

= 2.16 m/s

t =6s

This motion diagram shows two intervals of motion. Interval one is shown by the 6 long displacement vectors. Interval two is shown by the three shorter displacement vectors on the top.

Interval 1

Xi =-3 m

Interval 1

Xf =11m

Interval 1

V =

14m/6 s

=2.3m/s

t =6s

Interval 2

Xi = 11 m

Interval 2

Xf =7m

Interval 2

V =

-4m/3 s

=-1.3m/s

t =3s

22. Read the motion description and create a motion diagram that matches the word description. Each element of the motion diagram represents one second. (one dot with a displacement vector represents one second).

Word Description

Motion diagram

An object begins in a positive position and moves to 0 in 3 seconds.

An object begins in a negative position. It moves in the positive direction for 4 seconds. It’s final position is negative.

An object begins in positive position and moves in the positive direction over 5 seconds.

An object begins at zero and moves in the positive direction over 4 seconds. Then, it moves at the same speed but in the negative direction for 5 seconds.

A object begins at a negative position. It moves in the positive direction for 3 seconds. Next, it moves at a slower speed in the same direction for 3 more seconds.