Analysis of Toy Car Motion: Velocity, Acceleration, and Position Over Time

In this laboratory investigation, our task was to determine the velocity, acceleration, and position of a moving toy car within a specified time frame. Each group was provided with a toy car, a spark timer, and spark tape. The spark timer produced dots on the spark tape at tenths of a second intervals, which we used to gather data for analyzing acceleration and velocity.

Materials:

• Spark tape
• Spark timer
• Toy car
• Flat surface
• Data recording tools
• Graph plotting tools

Background:

The lab involved applying fundamental physics formulas:

1. Velocity = Change in Distance / Time Taken
2. Acceleration = Change in Velocity / Time Taken

These formulas allow physicists to deduce various aspects about an object's motion, such as constant velocity, acceleration or deceleration, and the influence of weight on acceleration.

Our data collection and graph plotting were guided by these formulas, enabling us to draw conclusions about the toy cars' movements.

Procedure:

We began by attaching spark tape to each group member's toy car and passing it through the spark timer.

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Simultaneously, we initiated the car and the timer, collecting data for analysis. Each member repeated this process, creating three sets of distance values. We measured the distance between dots in millimeters and plotted them against elapsed time, representing a tenth of a second per dot. The total distance my toy car covered was 49.2 centimeters over 1.7 seconds, plotted in the position graph. For velocity, we recalculated the distances between individual dots without compounding them, as velocity is the change in distance over the change in time.

The velocity graph showed distances ranging from 20mm to 33mm in a tenth of a second. Lastly, for acceleration, we calculated the change in velocity over the change in time and plotted it. My acceleration graph ranged from zero to five meters per second squared.

This laboratory exercise allowed us to apply these physics concepts practically and gain insights into the motion of the toy cars.

Data Collected

Velocity

Acceleration

Data Analysis/Conclusion:

1. Trend-lines and hand-drawn graphs, with slopes calculated through linear regression:

   a. Position: 3.36×10−2 cm/s3.36×10−2cm/s b. Velocity: 1.087×10−1 mm/s1.087×10−1mm/s c. Acceleration: −9.44×10−2 m/s2−9.44×10−2m/s2

   The consistent linearity in the data indicates that the toy car maintains a constant rate of motion. If the data exhibited significant variation, it would suggest fluctuations in the car's velocity, resulting in scattered rather than linear data.

2. Over time, both velocity and position show a relatively consistent upward trend, while acceleration fluctuates between zero and five meters per second squared.
3. Comparative analysis between two individuals:

   a. Position:

   • Person 1: 0.0336
   • Person 2: 0.0442 Decrease of 0.0106 or a 23.98% decrease.

   b. Velocity:

   • Person 1: 0.1087
   • Person 2: 0.2043 Decrease of 0.0956 or a 46.79% decrease.

   c. Acceleration:

   • Person 1: -0.0944
   • Person 2: -0.0621 Decrease of 0.0323 or a -52.01% decrease.
4. Variations in numbers among group members may result from discrepancies in measurements and other factors. Precise measurements and uniform procedures could lead to more closely aligned data.
5. Potential errors in data may arise from inaccurate measurements, obstructions during trial runs, and differences in spark-tape lengths. To enhance accuracy, standardizing procedures is essential—ensuring uniform spark-tape lengths, measurement methods, calculations, and graph intervals.
6. If a 20g mass is added to the car, one would anticipate a slower acceleration and increased velocity. The car would likely cover less distance in a given time compared to its performance without the added weight.