A car is travelling with a constant speed of 80km/h and passes a stationary motorcycle policeman. The policeman sets off in pursuit, accelerating to 80km/h in 10 seconds reaching a constant speed of 100 km/h after a further 5 seconds. At what time will the policeman catch up with the car?

IT IS 17.5 S

Car travels at 80km/h (22.222m/s).
Car would have travelled 333.333m after 15 seconds.

Bike sets off from rest to 80km/h (22.222m/s) in 10s. This is acceleration of 2.222m/s².

Then from 80km/h (22.222m/s) to 100km/h (27.778m/s) in 5s. This is acceleration of 1.111m/s².

Distance travelled in first acceleration is (s=ut+½at²)

s1 = 0 + ½*2.222*10²
s1 = 111.111m

Distance travelled in second acceleration is (s=ut+½at²)

s2 = 22.222*5 + ½*1.111*5²
s2 = 125m

Total distance travelled in 15s by the bike is then

s1 + s2 = 236.111m

Which is 333.333m - 236.111m = 97.222m from the car in the first 15s.

The bike advancing at 20km/h (5.556m/s) to the car which would take another

t = s/v = 97.222 / 5.556 = 17.50s

to catch up.

Total time is therefore 15 + 17.5 = 32.50s