Question

Two cars A and B travelling in the same direction and stopped at a highway traffic sign. As the

signal turns green car A accelerates at a constant rate of 1m/s2. Two seconds later the second

car B accelerates at constant rate of 1.3m/s2. When will the second car B overtakes the first

car A.

Answer 1

For the first car A

$s=a_1(t+2)^2/2$

For the second car B

$s=a_2t^2/2$

So we have

$a_1(t+2)^2/2=a_2t^2/2\to -0.3t^2+4t+4=0\to t=14.27\ (s)$

The second car B overtakes the first car A after 14.27 s from the beginning of its own movement, or

16.27 s after the start of movement of car A.