How much time is required for the entering car to catch up with the other car?

A race driver has made a pit stop to refuel. After refueling, he starts from rest and leaves the pit area with an acceleration whose magnitude is 5.4 m/s2; after 3.8 s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant velocity of 68.9 m/s overtakes and passes the entering car. The entering car maintains its acceleration. How much time is required for the entering car to catch up with the other car?
How much time is required for the entering car to catch up with the other car?
t = time to catch up

constant speed car distance traveled in (t) = 68.9t

velocity of accelerating car at main speedway entrance = (3.8)(5.4) = 20.5 m/s

accelerating car distance traveled in (t) = Vi(t) + 1/2(5.4)t虏 = 20.5t + 2.7t虏



set distances traveled by the two cars equal

68.9t = 20.5t + 2.7t虏

cancel t's

68.9 = 20.5 + 2.7t

2.7t = 68.9 - 20.5 = 48.4

t = 48.4/2.7 = 17.9 s ANS