Question

A speeder is driving down the road at a constant 20 m/s, he passes a patrolman parked on the roadside. The patrolman waits 3 seconds, then pursues the speeder, accelerating at a constant 4.0 m/s. How long does it take the patrolman to catch the speeder? How far has he traveled before doing so?
s=v(t+3)
s=at²/2
v(t+3) =at²/2
at²-2vt-6v=0
t²-10t-30=0
t=12.42 s
s= v(t+3)=20(12.42+3) = 308.4 m
Can you PLEASE explain how you got this answer?

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