Motion of a Toy Car
Introduction
Describing the motion of an object is an essential step in understanding how things move and eventually why things
move as they do. In this activity you will observe the motion of a toy car. You will gather data, organize that data in
tables and graphs and create an equation that can be used to describe the motion of the car. From the questions that
follow, you will distinguish between an instant in time and time intervals, between position and distance traveled, and
between speed and velocity.
Essential Question: How can the graph of distance traveled and time data be used to predict the motion of a moving
object?
Pre-Lab Exercise: Prior to doing the experiment, the teacher will demonstrate the safe use of the equipment. Based on
this demonstration, answer the pre-lab questions before continuing to the procedure.
Materials
Toy Car
Meterstick or Measuring Tape
Masking Tape or Dry Erase Marker
Timer (stopwatch, student cell phone, …)
Graph Paper
Procedure: Collect time and position data of the traveling car.
1. How many batteries does your car have? Write this information in your data table.
2. Use the meterstick and masking tape to mark out a track in half meter increments covering a total of 3.0 meters.
3. As demonstrated by your teacher, release the car from well behind the 0-meter starting line and start your timer
when the car crosses the starting line (0.00 meters). Record the instant in time when the car crosses each half
meter mark (0.5 meters, 1.0 meter, 1.5 meters, and on through 3.0 meters position). To do this efficiently will
require some student planning. If cell phones are allowed, using multiple timers may improve your efficiency and
results.
4. Record your position (df) and instantaneous time (tf) data in the table provided.
Analysis: Creating a graph and an equation for position based on instantaneous time.
5. Motion data is traditionally graphed with time plotted on the x-axis. Use this convention and graph your Position
versus Instantaneous Time data.
6. Add a best fit line to your graph and extend that line to the y-axis.
7. The following steps should be recorded in your student response sheet. This analysis is referred to as a Four Step
Method for generating an equation from a linear graph.
I.
Write down the slope intercept equation for a straight line as you learned in algebra, y=mx+b.
II.
In this generic math equation, replace the symbols for the y-axis and x-axis with the appropriate symbols from
your experiment. Some textbooks use (d) for position and (t) for time. The subscripts “f” for final and “i” for
initial are also commonly used. So, the coordinates for the final position are written (tf, df).
III.
Now replace the generic symbols for the constants of slope (m) and the y-intercept (b) with the actual slope
and y-intercept values from your best fit line on your graph of Position vs Time. Show how you calculated the
slope for your best fit line. Include all of the units for the slope and the y-intercept. Recall that the y-intercept
is the value of the equation when the x-value is zero. If the y-intercept (b) is zero or logically should be zero,
simply remove this symbol. In this activity, the intercept should be zero since the timer starts (ti=0) at the
initial position (di) zero.
IV.
Look at the units of your slope. What do we call the quantity that has the units of your slope? Rewrite the
equation again, replacing the slope with a symbol (letter) that represents this quantity.
8. Answer the questions in the student response section of you handout.
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Describing the Motion of a Toy Car
Pre-Lab and Data Sheet
Name
Partner(s)
Pre-Lab Questions: The following predictions are based on the teacher demonstration of the toy car.
1. In the space provided below, sketch a prediction for the Position vs Time graph for your toy car.
2. What will the Speed vs Time graph look like? Add this sketch in the space below.
Position Prediction
Speed Prediction
Data Table: The initial position is 0.00 meters when the timer starts at 0.00 seconds
My Car.
Neighbor’s Car (Question #10)
Final Position (m)
Number of Batteries =
Number of Batteries =
Instant in Time (S)
Instant in Time (S)
0.00
0.00
0.00
0.50
1.00
1.50
2.00
2.50
3.00
Analysis: Use the space below to write responses to the Four-Step Analysis in step 7 of the Analysis.
1.
2.
3.
4.
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Questions
1. How does your graph of the toy car’s position versus time compare to your prediction? Explain any
differences.
2. Use your graph and curve fit to determine the position of the car when the timer is at 6.0 seconds.
Circle this point on your curve fit line.
3. Use your equation from the Analysis step 7 (III) to determine the position of the car at 6.0 seconds.
Show the calculation including units.
4. Compare the results from questions 2 and 3.
5. At 6.0 seconds, is your car traveling up a hill, down a hill, or on a level surface? Explain your answer.
6. From the best fit line of your position graph, what distance did the car travel between the “clock
times” of 2.0 and 6.0 seconds? Describe how you determined the distance and mark these reference
points (instants) on your line.
7. Use your equation from the Analysis step 7 (IV) to determine the distance the car traveled between the
clock times of 2.0 and 6.0 seconds. Show your work for this calculation.
8. Compare the results from question 6 and 7.
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9. How would your Position graph change if you were given a faster car? A slower car? On the axis
provided, sketch the three motions. No numbers are needed. Label the cases as: Our Car, Faster Car,
and Slower Car.
10. Find a neighboring group with a car that had a different number of batteries than your car and collect
their instantaneous time data in the column titled Neighbor’s Car. In the data table, make sure you
indicate the number of batteries in each car.
11. Based on the number of batteries, what will a Position graph of their data look like compared to your
data? Add the labels “One Battery” and “Two Batteries” to the appropriate lines in your sketch for
question 9 above. For example, is the line Our Car the one battery or two batteries cars?
12. Use the data table for both cars to confirm your prediction for which car is faster. Cite the specific time
and position data points used to support this argument and show any calculations you may have made.
13. Add the new data set to your detailed graph of Position vs Instantaneous Time that you made in step
five in the Analysis section. Include a best fit curve for this new data.
14. Based on information in the graph, determine which of the two cars has the greater speed. Explain
how you used your graph to make this decision.
15. On a sheet of graph paper, draw a Speed vs Time graph for your car. Use the same time scale for the xaxis that you used for your Position vs Time graph. Now add a line for the Speed of your neighbor’s
car. Label the graph to indicate the line for your car and for the neighbor’s car.
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16. Explain any differences between the shape of this Speed graph for your car and your prediction in the
pre-lab.
A closer look at the Speed vs Time graph
Consider the relationship between the Position versus Time graph created from your data and the Speed
versus Time graph that you derived from the Position vs Time graph. Specifically, the Speed vs Time graph
was based on the slope (change in position divided by change in time) from the Position vs Time graph. One of
the great mathematical innovations from physics, was the realization that the process of finding speed from a
graph of position and time is reversible. In this case, the Speed vs Time graph can be used to find distances.
Essential Question: How can the Speed vs Time graph be used to determine the distance the car traveled
during a given amount of time?
Procedure
1. On your Speed versus Time graph, draw a vertical line that starts on the time axis at the 4.0 second
mark and ends on the line representing the speed of your car.
2. Now look at the rectangle created by the y-axis, the x-axis, the line representing the speed of the car,
and the vertical line you just added. Lightly shade in this rectangle.
In the four-step analysis, you learned to create an equation using the slope from a line and the variables
plotted on the axis of the graph. Now, you will use a similar process to create an equation from the area
between a data line and the x and y axis.
3. What math equation would you use to determine the area of this rectangle? Write this equation in the
space provided in the table below.
4. Now replace the generic variables in your math area equation with the axis labels from your graph.
Write this new equation in the space provided. For example, the bottom of the rectangle is on the
time axis, so use the variable (t) for this side of the rectangle. What symbol will you use for your speed
line?
5. Use this new area equation to find the area on your graph when t is 4.0 seconds and speed is the speed
of your car. Show your steps for this calculation and make sure you include the units for time (s) and
speed (m/s) in your written calculation. What are the units for the area on your graph when you
multiply the speed (m/s) by time (s)?
6. Now look back to your Position vs Time graph. What distance has the car traveled after 4.0 seconds
and how does the distance traveled after 4.0 seconds taken from your Position vs Time graph compare
to the area after 4.0 seconds on your Speed vs Time graph?
7. Based on this comparison and the units of measure found when you calculated the area under your
speed versus time graph, what information does the area on a speed versus time graph represent?
What symbol or variable would you use to represent this area?
Math Area
Equation
Area Equation
Speed vs Time
Area=
Area=
Show Calculation From the Position vs
Area at (t=4.0 s) Time graph, Distance
Include units
traveled after 4.0 s
Final Equation in Physics
Symbols for Area on a
Speed and Time Graph
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