Three toy cars D, E, and F are released from rest on the same straight track. Each car experiences a constant forward acceleration for a specified time, after which its motor shuts off and the car coasts at constant velocity.
Acceleration stage for each car:
Car
Constant acceleration a (m/s2)
Duration Δt (s)
D
1.5
4.0
E
2.0
3.0
F
0.80
6.0
Assume all cars have zero initial velocity at t=0.
a. Part 1: (a) Calculate the magnitude of the final velocity acquired by each car at the instant its motor shuts off. Show your work and include appropriate units.
b. Part 2: (b) Rank the cars by the magnitude of that final velocity, greatest to least.
c. Part 3: (c) Describe how the area under an acceleration–time graph for each car could have been used to reach the same ranking without explicit calculation.