Question

an automobile moving at a constant velocity of 50 ft/sec passes a gasoline station. 3 sec later, another automobile leaves the gasoline station and accelerates at the constant rate of 6.5 ft/sec2. how soon will the second automobile overtake the first?

Answer 1

Let t be the time after the constant-velocity car passes the station.

Require that they travel the same distance at time t
50 t = (1/2)*(6.5)(t-3)^2

Solve the resulting quadratic equation for t, which must exceed 3 s.