a speeding car is driving at 120 km/h when it passes a police cruiser that is driving at 100 km/h. One second later, the police cruiser accelerates uniformly at 15 km/h until it reaches a speed of 135 km/h. how long does it take the police cruiser to catch the car

Answer 1

You acceleration has the wrong units. Did you mean 15 kph/s or kph/hr?
Either way the car is only about 5.55 m ahead when the police car starts speeding up
xcar = vcar t + 5.55
xpol = vpol t + 1/2 a t^2
set equal to each other and solve