Question

Car A has 4 times the maximum acceleration of Car B. If they race (starting from rest) and both travel at their maximum acceleration, how do their final velocities compare when they pass the finish line?

a) They both have the same velocity at the finish line.

b) The velocity of Car A at the finish line is 2x that of Car B at the finish line.

c) The velocity of Car A at the finish line is 4x that of Car B at the finish line.

d) The velocity of Car A at the finish line is 8x that of Car B at the finish line.

e) The velocity of Car A at the finish line is 16x that of Car B at the finish line.

Answer 1

The motion of both cars is governed by the kinematics equations for uniformly accelerated motion. The two cars travel the same distance from start to end of the race. Let the distance traveled in the race be s. We want to find the velocity of the cars at the finish line when both cars keep accelerating at constant acceleration throughout the race. To find final velocity we use the following kinematics equation

Given both cars starts from rest, their initial velocities are zero, u=0.

Let the acceleration of car B be a_{​​​​​​B}, the velocity of car A is

a_A=4a_B

The final velocity of car B is

The final velocity of car A is

_{(b) The velocity of car A at the finish line is 2× that of car B at the finish line.}