A car and a truck are initially moving in the same direction at 20m/sec with the truck 38m ahead. The car accelerates at a constant speed of?

Question

A car and a truck are initially moving in the same direction at 20m/sec with the truck 38m ahead. The car accelerates at a constant speed of 2m/sec², passes the truck, and returns to the left lane when it is 11m ahead of the truck. how far has the truck moved in this time?

Answer 1

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Answer: 140m

Observe motion of car relative to truck.

For observer in truck, initially they both seem at rest, then car starts to accelerate and moves from 38m behind to 11m in front, apparently covering distance s = 38 + 11 = 49m.

The time required is

t = sqrt(2s/a)

t = sqrt(2*49/2) = 7s

The whole event happened in 7s.

For stationary observer on roadside, real distance that the truck covered was

s_t = v t = 20 * 7 = 140m

Distance for car

s_c = v t + a t^2 / 2

s_c = 20 * 7 + 2 * 7^2 / 2 = 140 + 49 = 189 m