Acceleration practice worksheet with car and stick figure motion scenarios.

1. The car's acceleration is calculated using the formula: Acceleration = (V_final - V_initial) / time.
- V_initial = 0 m/s (at t = 0.00 sec)
- V_final = 26.94 m/s (at t = 3.34 sec)
- Time interval = 3.34 sec - 0.00 sec = 3.34 sec
- Acceleration = (26.94 m/s - 0 m/s) / 3.34 s = 8.07 m/s²

2. Yes, the person accelerated. The evidence is that their velocity increased over time: from 0 m/s at t=0 sec to 12.52 m/s at t=3.87 sec, then to 17.88 m/s at t=6.54 sec, and finally to 31.29 m/s at t=8.77 sec. Since velocity changed, acceleration occurred.

3. Completed table:
- Interval A:
- Average Time to go through the interval (s): (3.87 + 0) / 2 = 1.935 s
- Velocity at the beginning of the interval (m/s): 0 m/s
- Velocity at the end of the interval (m/s): 12.52 m/s
- Acceleration in the interval (m/s²): (12.52 - 0) / (3.87 - 0) = 3.235 m/s²
- Interval B:
- Average Time to go through the interval (s): (6.54 + 3.87) / 2 = 5.205 s
- Velocity at the beginning of the interval (m/s): 12.52 m/s
- Velocity at the end of the interval (m/s): 17.88 m/s
- Acceleration in the interval (m/s²): (17.88 - 12.52) / (6.54 - 3.87) = 2.007 m/s²
- Interval C:
- Average Time to go through the interval (s): (8.77 + 6.54) / 2 = 7.655 s
- Velocity at the beginning of the interval (m/s): 17.88 m/s
- Velocity at the end of the interval (m/s): 31.29 m/s
- Acceleration in the interval (m/s²): (31.29 - 17.88) / (8.77 - 6.54) = 6.013 m/s²

4. On graph paper, plot a velocity vs. time graph with time (s) on the x-axis and velocity (m/s) on the y-axis. Plot points at (0, 0), (3.87, 12.52), (6.54, 17.88), and (8.77, 31.29). Connect these points with straight line segments to form a piecewise linear graph.

5. The slope of each segment of the velocity vs. time graph equals the acceleration calculated for that corresponding time interval. For example, the slope of the segment between t=0 and t=3.87 sec is (12.52 - 0)/(3.87 - 0) = 3.235 m/s², which matches the acceleration calculated for Interval A. This relationship holds for all segments.