Question

Car A is traveling at 20.0 m/s and car B at 27.0 m/s.
Car A is 300 m behind car B when the driver of car A
accelerates at 2.10 m/s2. How long does it take car A to
overtake car B?

Answer 1

Take the moment car A starts to accelerate to be the origin. Then car A has position at time t

x = (20.0 m/s) t + 1/2 (2.10 m/s²) t²

and car B's position is given by

x = 300 m + (27.0 m/s) t

Car A overtakes car B at the moment their positions are equal:

(20.0 m/s) t + 1/2 (2.10 m/s²) t² = 300 m + (27.0 m/s) t

300 m + (7.00 m/s) t - (1.05 m/s²) t² = 0

==>  t ≈ 20.6 s