Question

A student driving at a constant speed of 45 m/sec passes a highway patrol car parked on the side of the road. One second later, the patrol car accelerates at a constant rate of 3.00 m/sec^2 in an attempt to catch up with the speeding student. How long does it take to over take the student?

Answer 1

After one second, when the patrol car is at location x = 0, the student is at 45 m.

The student's location as a function of time, where t=0 when the police car starts accelerating is

45 + 45*t

The policeman's position is

1/2*3*t^2

Set these two equations equal to each other and solve for t