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Determining Velocity, Acceleration and Distance: Car Example

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Two cars are racing. Car A starts L=15m ahead of Car B. Car B starts with an initial velocity of v_bo=5m/s, Car A starts from rest. Car A accelerates with a_A=2m/s2, and Car B accelerates with a_B=1.5m/s2.

a) Give the equations of motion for each car, assuming that x = 0 refers to the starting point of Car B.
x_A(t) = __________
x_B(t) = __________

b) What are the positions and speeds of each car at t=2s?
x_A(t=2) = __________
x_B(t=2) = __________
v_A(t=2) = __________
v_B(t=2) = __________

c) Does Car B ever catch up with Car A? If so, when and where?
x_catch-up = _________
t_catch-up = _________

d) If they race to a point of distance D from the origin, and it takes 20 seconds for the winner to get to D, who wins the race, and what is D?
winner = _________
D = _________

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Solution Summary

Solution provides steps necessary to determine velocity, acceleration and distance.