posted by Harry on .
A race driver has made a pit stop to refuel. After refueling, he leaves the pit area with an acceleration whose magnitude is 6.0m/s 2 . After 4.0s he enters the main speedway. At the same instant, another car on the speedway and traveling at a constant speed of 70 m/s overtakes and passes the entering car. If the entering car maintains its acceleration, how much time is required for it to catch the other car?
Measure time from the instant the pit car (#1) enters the speedway. When that car enters, its speed is 6.0 * 4.0 = 24 m/s, and it is still accelerating.
X1 = Vo t + (1/2) a t^2 = 24t + 3 t^2
For the constant-speed car,
X2 = 70 t
The time required for car 1 to catch up with car #2 is given by
X1 = X2
24t + 3 t^2 = 70t
46t = 3 t^2
t = 0 or 46/3 s
We are not interested in the t=0 solution, therefore
t = 15.3 s