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**Grades:** 6-8

**Author:** Sandy Van Natta

**Source:** The Motion of a Battery Powered Car - taken from OSCI 7-10 Physical Science Materials developed in 2005

Students use the variables of time and distance traveled to observe the characteristics of a distance vs time graphs for the motion of a battery powered car operating with one battery then again with two batteries. This allows students to explore how the number of batteries used to power the car affects the characteristics of distance vs time graphs. Students then use the time and distance data collected for the motion of the cars in the two trials to calculate the average speed of the car in each case. The average speeds will then be compared to the slopes of the respective distance vs time graphs.

**What should students know as a result of this lesson?**

- Students will know that speed or velocity is determined by the amount of distance covered by an object in a given amount of time.
- Students will know that a reference point is need in order to measure distances and direction covered by a moving object.
- Student will know that a battery driven car moves at a constant velocity, however, the overall average velocity of the car will depend on the number of batteries used to power the car.
- Students will be able to relate the slope of a line on a distance/time graph to the average velocity of their car.

**What should the students be able to do as a result of this lesson?**

- Student will collect distance and time data for a battery driven car.
- Students will construct graphs from their data.
- Student will draw the "best fit" straight line to fit the points plotted on their graphs.
- Students will be able to describe the motion of their battery driven car.

**For Getting Ready:**

- One battery powered car per group - inexpensive cars are available at toy stores. Cars are also available through science supply catalogs.
- 2 batteries - the correct size needed to fit the car
- Wire
- Wire cutters and strippers (for teacher use only)
- Optional - a metal bar cut to the length of the battery size needed

**For the Engagement:**

- A small wind-up toy

**For the Procedure:**

- Masking tape
- Meterstick
- Battery powered car - prepared in getting ready
- 6 Stopwatches
- Graph paper
- Ruler

**Getting Ready:**

- For Part A, prepare a wire for each car that is slightly longer than the length of the battery needed to fit the car. If the wire is insulated, remove about 1 cm of insulation from each end.
- Put one battery and one wire in the battery case of each car. Make sure the wire makes contact with the metal contacts of the battery holder so that the car will "run" on one battery. (A metal bar the length of the battery can be used instead of the wire.
- For Part B, put two batteries in each car

**Engagement**

Set a small wind-up toy in a central location where is can be seen by students. Wind the toy up and allow it to move across a smooth level surface. Pick the toy back off the surface before it can begin to slow to a stop. Ask students to describe the motion of the toy. Most students will say that the toy is moving at a constant rate for most of its "run". (The toy does "speed up" as it first starts off but most of its motion will appear to be at a steady rate.) Ask the students how they could prove that the toy was moving at a constant rate. Help your students figure out that they would have to know how far the toy traveled in a given amount of time, then compare equal time periods, in order to accurately describe the motion of the toy.

*Assessment:* Try to involve all students in the discussion. Ask students to give examples of objects observed in their daily lives that might be moving at a constant rate.

**Exploration**

__Part A: One Battery Car__

- Place 7 students in a group.
- Tape a 10 cm piece of masking tape on the floor. Mark this tape as the starting line or d = 0.
- From the starting line, measure out 100 cm and place a second 10 cm tape. Label this tape 100 cm.
- Measure out another 100 cm and place a third 10 cm piece of tape. Label this tape 200 cm.
- Continue placing and labeling tape every 100 cm until the last tape reads 600 cm.
- Position one student holding the car at the starting line. Position the other 6 students, each with a stopwatch, at each of the 100 cm marks. Be sure that all the stopwatches are set at 0.00 sec
- Without running the stopwatches, have the student holding the car start its electric motor and release it from the starting line. Ask the students to watch the car as it passes over each marked piece of tape. Ask them to describe the motion of the car and say if the car is moving fast or slow.
- Return the car to the starting position. This time ask the students to time the car as it moves along its path. Have the student with the "running" car hold the front wheels about 3 cm above the starting line and call out "ready, Set, Go". On "Go" the car should be set down and released on the starting line and all other students should start their stopwatches.
- As the car passes each distance mark, the student at that mark should stop his/her stopwatch.
- Record the times in column 1 of the data table (under Trial 1).
- Reset all stopwatches to 0.00 sec. Bring the car back to the starting line and repeat steps 8 and 9. Record the times in column 2 on the data table (under Trial 2).
- Repeat step 11 for Trial 3 and record the data in column 3.
- Calculate the average time of the three trials for each distance. Record the averages in column 4 of the data table.
- Calculate the time the car traveled each 100 cm distance. Record the time for each 100 cm distance in column 5 of the data table.
- On a piece of graph paper, plot the Total Distance (cm) versus the Average Time (sec).
- Using a ruler, draw the "best fit" straight line through your points. Do not worry if the line does not touch all the points.

__Part B: Two Battery Car__

- Put a second battery in the battery case of the car.
- Repeat steps 8 through 14 from Part A recording all the data in the second data table.
- On the same piece of graph paper that has the plot of the data from Part A, plot the Total Distance versus the Average Time data for Part B. Use a different color to plot these points. Draw the "best fit" line to fit the second set of data points.

__Part C: Average Speed__

- The following calculations should be made for both Part A and Part B data tables. Using the formula, average speed = distance/time (vavg = d/t), calculate the average speed for each 100 cm distance. This can be done by dividing 100 cm by each of the times in column 5. This gives the average speed of the car for each 100 cm distance. Record the average speeds in column 6 of the tables.
- Calculate the average speed of the entire run in both Part A and Part B. Again use the formula vavg = d/t but this time divide the 600 cm by the time it takes the car to reach the 600 cm tape.
- Calculate the slope of each line on the graph. Choose two points that are on the line and as far apart as possible. Circle the chosen points. Write the coordinates of each point next to the circle. The time should be listed first in the ordered pair. Use the formula slope = (d2 - d1)/(t2 - t1) for each line.

*Assessment:* See that students are following proper laboratory procedures. Make sure each group is recording all their data and constructing their graphs.

**Explanation**

Discuss the student's observations and graphs. Help students gain the following understanding. "How far?", How long?", and "How fast?" are questions asked when motion is studied. For example, if a 100 m dash in a track and field event is watched, the observer wants to know how long the race was? - 100 m; how long it took to run the race? - about 9.8 seconds; and what was the average speed of the runner? - 10.2 m/sec. The motion of a car can be described by measuring the distance and time to calculate the speed.

__How Far? - Distance__

In order to determine the distance traveled by an object, you first have to establish the car's location (position) as well as its direction. A reference point from which distances can be measured must be selected. In this activity, the first reference point is the starting position which is labeled d=0. This position, along with the other marks made at 100 cm intervals in a straight line, provides a reference frame to be used to determine the car's location. The distance traveled is the change from one position to another relative to our frame of reference. This change in position is also called displacement. Displacement is a distance and the direction of the changing position of an object.

__How Long? - Time__

When the car is at the starting position of d=0, the time is also 0. The car and the stopwatches were started at the same time. Every time the car passes one of the reference marks at every 100 cm, the time on the stopwatch is recorded. The time for a particular distance traveled is the time recorded for that reference mark at that distance from d=0. To find the time interval between any two reference marks (for example from the 100 cm mark to the 200 cm mark), subtract the time recorded at the 100 cm mark from the time recorded at the 200 cm mark. This will be the amount of time needed to travel the 100 cm from the 100cm to the 200 cm mark.

__How Fast? - Speed or Velocity__

As the observer watches the car move across the frame of reference, he/she can decide qualitatively whether the car is moving fast or slow. Calculating a numerical value for the speed of the car gives a more precise meaning to the terms fast or slow. The average speed of the car can be found by dividing the distance traveled by the time needed to travel that distance.

vavg = d/t

vavg stands for average speed or velocity. Speed is actually a scalar quantity that only tells how fast an object is moving. Velocity is a vector quantity that tells not only how fast an object is moving but also what direction the object is moving. Once values for vavg have been calculated, it is easy to determine which car is moving faster or slower. The car with the greater numerical value for vavg is moving faster than the car with the lower value.

When graphs of the cars' motion are plotted, the data points will produce nearly a straight line. This indicates that both time and distance are changing at a steady rate. The car is moving at a constant speed. The line with the steepest slope represents the car moving with the higher speed. The numerical value of the slope equals the average speed of the car.

*Assessment:* Collect and evaluate the students' data sheets and graphs.

**Elaboration**

Have students design an experiment to determine the velocity of another object moving at a constant speed such as the wind-up toy use in the Engagement section. Or, students may want to predict what would happen to the speed of the battery car if it moved up an inclined plane. If inclined planes are used, they should be at least 1 to 2 meters long so students can record as many data points as possible. However, distances used will need to be measured in much smaller increments than 100 cm. This will depend on the speed of the car and the length on the inclined plane. Distances of 25 cm may be tried. Note: the car will still move up the inclined plane at a constant velocity. However the overall average velocity will be less than that on a car moving on a level surface.

*Assessment:* Students should write out the procedures, data tables, and data relating to their experiment. They should construct graphs to represent their results. Using their data and graphs as evidence, students should write a conclusion relating to the motion of their car or toy under the circumstances studied.

Students need to be able to make measurements with metersticks and stopwatches. Students should be able to create graphs using x and y coordinates and find slopes of lines.

- Learning Cycle
- Hands-on/Minds-on Learning
- Inquiry

**NGSS Standards:**

- MS-PS2-2 Plan an investigation to provide evidence that the change in an object's motion depends on the sum of the forces on the object and the mass of the object.
- MS-PS3-1 Construct and interpret graphical displays of data to describe the relationships of kinetic energy to the mass of an object and to the speed of an object.

**Common Core Standards:**

- RST.6-8.1 Cite specific textual evidence to support analysis of science and technical texts.
- RST.6-8.3 Follow preciesly a multistep procedure when carrying our experiments, taking measurements, or performing technical tasks.

**National Standards:**

- Content Standard A: 5-8 Science as Inquiry
- Content Standard B: 5-8 Physical Science

**Ohio Standards:**

- Grades 6-8 Physical Science Benchmark B
- Grades 6-8 Scientific Inquiry Benchmark A
- Grades 6-8 Scientific Inquiry Benchmark B

If time and distance are changing at a steady rate, an object is moving at a constant velocity. Such motion can be plotted on a graph (time on the X axis and distance on the Y axis) and produces a straight line with a positive slope. The slope of the line is the numerical value of the average speed of the object. The steeper the slope, the greater the overall average velocity of the object.

No special safety or disposal procedures are required.

Whenever an object is moving at a constant speed in a given direction it has a constant velocity. A car in cruise control moving on a freeway or a walker moving with a steady even pace covers equal distances in comparative amounts of time. These are examples of objects moving with a constant velocity.

Give student a series of distance vs. time graphs representing the motion of moving objects. Some of the graphs should show straight lines with positive slopes. Others may have curved lines or horizontal lines. Ask students to pick out the objects moving at constant velocities (the graphs showing straight lines with positive slopes) and determine the average speeds of each object from the data presented.

**Grouping Suggestions** Try to place students with varying backgrounds and abilities in each group. Having a student with strong mathematical skills in each group will help with the groups' calculations.

**Pacing/Suggested Time:** Getty ready will take about 15 minutes. The remaining activity should take about 90 minutes to complete.