constant velocity worksheet 1 - monroe.k12.nj.us€¦ · web viewconstant velocity worksheet 2....

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Constant Velocity Worksheet 1

1. Consider the position vs. time graph below for cyclists A and B.

a. Do the cyclists start at the same point? How do you know? If not, which is ahead?

b. At t= 7s, which cyclist is ahead? How do you know?

c. Which cyclist is travelling faster at t = 3s? How do you know?

d. Are their velocities equal at any time? How do you know?

e. What is happening at the intersection of lines A and B?

©Modeling Workshop Project 2004 1 Unit II v3.0

x(m)

t (s)

A

B

5 s


2. Consider the new position vs. time graph belowfor cyclists A and B.

a. How does the motion of the cyclist A in the new graph compare to that of A in the previous graph from page one?

b. How does the motion of cyclist B in the new graph compare to that of B in the previous graph?

c. Which cyclist has the greater speed? How do you know?

d. Describe what is happening at the intersection of lines A and B.

e. Which cyclist traveled a greater distance during the first 5 seconds? How do you know?


x(m)

t (s)

A

B

5 s

New Graph x(m)

t (s)

A

B

5 s

Previous Graph


Constant Velocity Worksheet 2Draw the velocity vs time graphs for an object whose motion produced the position vs time graphs

shown below at left.

1.

2.

3.



Sketch velocity vs time graphs corresponding to the following descriptions of the motion of an object.

4. The object is moving away from the origin at a constant (steady) speed.

5. The object is standing still.

6. The object moves toward the origin (position = 0) at a steady speed for 10s, then stands still for 10s.

7. The object moves away from the origin at a steady speed for 10s, reverses direction and moves back toward the origin at the same speed.




1. Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the times listed below:

t (s) x (m)

0.0 10.0

1.0 12.0

2.0 14.0

5.0 20.0

8.0 26.0

10.0 30.0

a. Plot a position vs. time graph for the skater.

b. How far from the origin (position = 0) was he at t = 6s? How do you know?

c. Write a mathematical model (equation) to describe the graph in (a).

d. Was his speed constant over the entire interval? How do you know?



2. The following data were obtained for a second trial:

t (s) x (m)

0.0 4.0

2.0 10.0

4.0 16.0

6.0 22.0

8.0 28.0

10.0 34.0

a. Plot the position vs. time graph for the skater.

b. How far from the origin was he at t = 5s? How do you know?

c. Was his speed constant? If so, what was it?

d. In the first trial the skater was further along at 2s than he was in the second trial. Does this mean that he was going faster? Explain your answer.



3. Suppose now that our skater was observed in a third trial. The following data were obtained:

t (s) x (m)0.0 0.0

2.0 6.0

4.0 12.0

6.0 12.0

8.0 8.0

10.0 4.0

12.0 0.0

a. Plot the position vs. time graph for the skater.

b. What do you think is happening during the time interval: t = 4s to t = 6s? How do you know?

c. What do you think is happening during the time interval: t = 6s to t = 12s? How do you know?

d. Determine the skater's average speed from t = 0s to t = 12s.

e. Determine the skater's average velocity from t = 0s to t = 12s.




1. Label positions and times on the motion map above, then answer the following:

a. What can you conclude about the motion of the object?

b. Draw a quantitative graphical representation of x vs t (see below).

c. Draw a quantitative graphical representation of v vs t (see below).

d. Write a mathematical expression that represents the relationship between x and t, from fig. 1.

e. Write a mathematical expression that represents the relationship between v and t, from fig. 2

f. Describe what the area under the curve in fig. 2 represents. Shade this area.


x

t

v

t


2. From the position vs time data below, answer the following questions.

t (s) x (m)0 01 22 43 44 75 106 107 108 59 0

a. Construct a graph of position vs time.

b. Construct a graph of velocity vs time.

c. Draw a motion map for the object.

d. Determine the displacement from t = 3.0s to 5.0s using graph B.

e. Determine the displacement from t = 7.0 s to 9.0 s using graph B.



3. Use the description of the motion given below to answer the following questions.

Starting at position x = 2 m, Bob walks in the positive direction at a constant speed of 3 m/s for 2 s, stops for 3 s and then moves in the negative direction at a constant speed of 1 m/s for 5 s.

a. Construct a graph of velocity vs. time.

b. Construct a graph of position vs. time.

c. What is Bob’s final position? How did you find it?

d. Draw a motion map for Bob in the space below. Label the axis and indicate which dot represents the position at t = 0.


X (m)



1. A bike travels at a constant speed of 4.0 m/s for 5.0 s. How far does it go?

2. The light from the Sun reaches Earth in 8.3 minutes. The speed of light is 3.00x108 m/s. How far is Earth from the Sun?

3. You and your friend each drive 50.0 km. You travel 90.0 km/h and your friend travels 95.0 km/h. How long will your friend have to wait for you at the end of the trip?

4. Two runners approaching each other on a straight track have constant speeds of 4.50 m/s and 3.50 m/s, respectively, when they are 100 m apart. How long will it take for the runners to meet, and

at what position will they meet if they maintain these speeds?



x vs t Graph v vs t Graph Written Description Motion Map

x

tv

t

x

t



Object moves with constant positive velocity for 4 seconds. Then, it stops for 2 seconds and returns to the initial position in 2 seconds.

Object A starts 10m to the right of the origin and moves to the left at 2 m/s. Object B starts at the origin and moves to the right at 3m/s.



Constant Velocity Review

1. Consider the position vs time graph at right.

a. Determine the average velocity of the object.

b. Write a mathematical equation to describe the motion of the object.

2. Shown at right is a velocity vs time graph for an object.

a. Describe the motion of the object.

b. Draw the corresponding position vs time graph. Number the x - axis.

c. How far did the object travel in the interval t =1s to t =2s?

d. What is the total displacement? Explain how you got the answer.



3. Johnny drives to Wisconsin (1920 miles) in 32 hours. He returns home by the same route in the same amount of time.a. Determine his average speed.

b. Determine his average velocity.

c. Compare these two values and explain any differences.

4. Consider the v vs t graph below.

a. Describe the behavior of the object depicted in the graph.

b. Draw a motion map that represents the behavior of the object.

5. A race car travels at a speed of 95 m/s. How far does it travel in 12.5 s? Use the appropriate mathematical model and show how units cancel. (Keep the proper number of sf's.)



In each of the following problems you are given the x vs. t graph, the v vs. t graph, the motion map or a written description of the motion of an object. Complete each by providing the missing items. Label all axes with appropriate scales!!

6.

Written Description:

7.



t(s) t(s)

t(s) t(s)

x(m) v(m/s)

x(m) v(m/s)

x(m)

0 10 0 10

0 10 0 10

10

0

0

-10

0 2 4 6 8

t=0

t=10


8.


9. Jim leaves home at noon and drives east on I-10 at 60 mph, Jenny leaves from the same location at 1:30 PM, but travels east at 70 mph. When and where will Jenny catch up to Jim?


t(s) t(s)

x(m) v(m/s)

0 10 0 10

4

0

-4

constant velocity worksheet 1 - monroe.k12.nj.us€¦ · web viewconstant velocity worksheet 2....

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