Question

Two bank robbers 1are in their get-way car traveling at it's top speed of 30m/s. They drive by a parked pollice officer who was on the lookout for them. If the police officer takes 2 seconds to react and engage in pursuit , how long will it take him to catch the robbers if his carhas a maximum acceleration of 4.5m/s^2. You assume the police officers car has a greater top speed than the robbers car

Answer 1

Of course you have to assume the cops can go faster than the robbers -- how else could they ever catch them?

t seconds after passing the parked car,
the robbers have traveled 30t meters
The cops have gone 1/2 * 4.5 * (t-2)^2
So, just solve
30t = 2.25 (t-2)^2

Answer 2

d1 = 30m/s * 2s = 60 m.

60 + 0.5a*t^2 = 30t.
2.25t^2 - 30t + 60 = 0,