INTERACTIVE PHYSICS
Student Worksheet Interactive
3 Relative Velocity and Acceleration
FIRST:
Student Directions and Worksheet
Physics Interaction 3
Relative
Velocity and Acceleration

Overview 
Objective

To learn how measurements of velocity and acceleration taken from different reference frames are related to each other. 
Summary of Interaction

First, you will be asked some questions to develop your intuition about these concepts. Then, you will observe “bandits” running atop “train cars” to record and analyze information about their relative velocity and acceleration. 
Formulas Required

1. vbe = vbt + vte (vector velocity addition) 2. abe = abt + ate (vector
acceleration addition) 3. vbe = –veb, abt = –atb and so on (vector
direction reversal) 4. v = (magnitude of velocity) 
Concepts Explored

Relative velocity Relative acceleration 

Activity A: Hopping on a Bus 

To get warmed up, answer the following questions. They are designed to focus you on the main concepts of this worksheet so that when you get to the experiments, your thoughts will be clearer. 
Problem 1 
Pretend that you are
walking from the back to the front of a bus. The bus is moving forward at
10 m/s, and you are walking in the bus at 1 m/s. How fast are you
walking relative to the ground? 
Problem 2 
Now pretend that you
are walking from the front to the back. The bus is still moving forward at 10
m/s, but you are walking 1 m/s toward the back. How fast are you now walking
relative to the ground? 
Problem 3 
Pretend that the bus
driver and an observer on the sidewalk have accurate stopwatches. They both
have agreed to time you as you walk from the back to the front of the bus,
recording how much time it took. Will both of their measurements agree? 

Activity B: Observing a Bandit’s Motion on a Train 



Now imagine that you have disembarked from the bus and have hopped on a train. A bandit has also hopped on the train, but bandits being as they are, he has hopped onto the roof. What you are going to do is record some information about the bandit’s velocity from different reference frames. 

1. Open the document Bandit on a Train. 

In this experiment, there is one bandit on the roof of one train car. However, you have been provided with two views of this scene. The first is from the point of view of an observer standing on the earth (observer E). The second is from the point of view of an observer moving along with the train (observer T). The view at the top is observer E’s view; the view at the bottom is observer T’s view. 

2. Run the experiment,
stopping it when the bandit reaches the end of the train car (approximately). 
Problem 4 
Are the two views of
the bandit consistent with each other? Specifically, would observer E and
observer T agree that the bandit reached the end of the train car after the
same amount of time? 

To analyze what you have observed, you will need to record information from the meters. Find the meter with the label “Velocity/Bandit to Train.” This meter indicates the velocity of the bandit relative to the train. Be sure to read the velocity in the xdirection (Vx). In this worksheet, the velocity of the bandit relative to the train will be represented by the symbol vbt. The velocity of the train relative to the earth will be represented by the symbol vte. 
Problem 5 
Record the value of the
bandit’s velocity relative to the train. 

Now record the velocity
of the train relative to the earth. 

Give some thought to what you have just observed. Think back to the story of hopping on the bus. You just recorded the velocity of the bandit relative to the train, and the velocity of the train relative to the earth. 

Given the quantities vbt and vte,
what prediction can you make about the velocity of the bandit relative to the
earth? Explain how you arrived at your answer. 
Problem 6 
Now look at the screen
at the meter with the label “Velocity/Bandit to Earth.” Record this value. 

Compare your prediction
of the bandit’s velocity to the recorded value. 

3. Close the document. 

Activity C: Observing the Bandit’s Relative Velocity 

This scenario is much like the one above; the difference is that the train has reversed direction. You will be focused on the relative velocity of the bandit as seen by observer E and observer T. 



1. Open the document Bandit on a Train 2. 

In this experiment, there is one bandit and one train, but you are provided with two views of the scene. The first view is from the reference frame of observer E (the observer on the earth) and the second view is from the reference frame of observer T (the observer moving along with the train). 

2. Run the experiment,
stopping it when the bandit reaches the end of the train car (approximately). 
Problem 7 
Are observer E’s and
observer T’s views of this scene consistent with each other? (Specifically,
would the two observers agree on the bandit’s position on the train car at
all points in time?) 
Problem 8 
Record the velocity of
the bandit with respect to the train. Remember to record the xcomponent of
velocity (Vx) only. 

Record the velocity of
the train with respect to the earth. 

Using the values of vbt and vte,
calculate the velocity of the bandit with respect to the earth. 
Problem 9 
Read the value of vbe from the meter. Compare the calculated
value of vbe to the value on the third
meter. 

3. Close the document. 



Activity D: Observing the Bandit’s Relative Acceleration 

This scenario is similar to the last, but the bandit will be accelerating relative to the train car, and the train car will be accelerating relative to the earth. 

1. Open the document Bandit on a Train 3. 

Again, there is one bandit and one train, but you are provided with two views of the scene. The first view is from the reference frame of observer E and the second view is from that of observer T. 

Note that a net force is acting on the bandit, and another net force is acting on the train car. The bandit is increasing his speed as he runs forward; the friction from the soles of his shoes provide the force forward. The train car is accelerating; the force is provided from the pull of the car in front. 

Note that there does not appear to be a net force acting on the train car from observer T’s point of view. This is because observer T is being accelerated along with the train and therefore does not observe the train accelerating relative to him. 

2. Run the experiment,
stopping it when the bandit reaches the end of the train car (approximately). 
Problem 10 
Are observer E’s and
observer T’s views of this scene consistent with each other? 
Problem 11 
Record the acceleration
of the bandit with respect to the train. Remember to record the xcomponent
of acceleration (Ax) only. 

Record the acceleration
of the train with respect to the earth. 

Using the values of abt and ate,
calculate the acceleration of the bandit with respect to the earth. 
Problem 12 
Read the value of abe from the meter. Compare the calculated
value of abe to the value on the third
meter. 

3. Close the document. 

Activity E: Observing the Bandit’s Relative Velocity and Acceleration 

In activities C and D, you focused on only one aspect of the bandit’s motion: his velocity or his acceleration. In this activity, you will be observing both of these measures simultaneously. 

1. Open the document Bandit on a Train 4. 

As before, there are two views of the same bandit. 

Before running the experiment, be prepared to watch the two velocity meters and the two acceleration meters as the bandit moves toward the end of the train car. You will be asked to record your observations. 

2. Run the experiment,
mentally comparing the two velocity meters and the two acceleration meters. 

3. Stop the experiment when
the bandit reaches the end of the train car (approximately). 
Problem 13 
Record the two values
of the acceleration of the bandit. 

Record the two values
of the velocity of the bandit. 

Is the acceleration of
the bandit as measured in one reference frame larger than the other? If so,
which measurement is larger, and how much larger is it? 

Using the recorded values of vbt and vbe, you should be able to determine vte. 
Problem 14 
Explain how to compute
vte given vbt
and vbe. Then compute vte. This will be referred to as your “first
calculation” since you will recompute it later. 

Using the values of abt and abe, you should be able to determine ate. 
Problem 15 
Explain how to compute
ate given abt
and abe. Then compute ate. 

From this computation
of the train’s acceleration with respect to the earth, is it correct to say
that the train and the earth are moving at a constant velocity with respect
to each other? 

4. Reset and rerun the
experiment. This time, stop it when the bandit is only halfway to the end of
the train car (approximately). 
Problem 16 
Read the values of vbt and vbe
at this point in time and use them to compute the value of vte. 

From your first and
second calculations of vte, is it
correct to say that observer T and observer E are moving at a constant
velocity relative to each other? 

5. Close the document. 

Additional Questions 

1. You are walking up an
escalator at a rate of 1 step per second. The escalator is running at a speed
of 0.5 steps per second. What is your effective climb
rate? Approximately how long will it
take you to ascend the equivalent of 15 steps? 

2. The water of the Gulat
River travels at a rate of 0.3 m/s. You paddle upstream at a rate of 0.7 m/s
relative to the water. What is your velocity upstream relative to the earth? 

3. An airplane is moving 600 mi/h
northward with respect to the earth. The winds are blowing to the south at a
rate of 20 mi/h with respect to the earth. What is the velocity of the plane
with respect to the air? 

4. A car is moving west along
the highway at a rate of 2 km/h. A bug is crawling directly across the roof
of the car from the driver’s window to the passenger’s window at a rate of
0.5 km/h. How fast is the bug moving with respect to the earth? 

5. At a certain instant in
time, a particle is accelerating upward at a rate of 3 m/s2 with respect to the earth. At the same time, it is
accelerating horizontally at a rate of 2.6 m/s2 with respect to the earth. What is the magnitude of its total
acceleration? 