Two gangsters, having just robbed Speedway, are flying down 1-70 West at a const

Question

Two gangsters, having just robbed Speedway, are flying down 1-70 West at a constant 108 km/hr. If they make it to Indiana, they'll be safe. When they are 1 km from the Indiana border, while still travelling at a constant 108 km/hr. they pass a concealed police car hidden in a speed trap. At the instant that the criminals pass the patrol car, the cop pulls onto the highway and accelerates at a constant rate of 2 m/s2. Does the cop catch up with them before they cross the state line? Since this is a warm-up problem, here are some things that you should consider What is the acceleration of the gangsters' car? What is the acceleration of the cop car? What are the initial velocities? How long will it take for the gangsters to get to Indiana? How long will it take the cop? Are there kinematic equations that are appropriate for use here?

Explanation / Answer

108kmph=30m/s

acceleration of gangster's car=0

acceleration of cop car=2m/s2

vgangster=30m/s

vcop=0m/s

time for gangsters to get to indiana=1000/30=33.33s (using second equation of motion with a=0 i.e. s=ut

time for cops to reach indiana=sqrt(2s/a)=31.62s (using second equation of motion with u=0 i.e. s=0+0.5at2)

Since cop car reaches border faster, it will catch the gangsters.

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