two gangsters, having just robbed speedway, are flying down i-70 west at a const

Question

two gangsters, having just robbed speedway, are flying down i-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?

Do this problem on your own and turn it in at the beginning of next week's recitation (due 1/23/14). 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? Your answer must be organized, clear, and include the elements of the problem solving path: Focus the Problem Describe the Physics Plan the Solution Execute and Evaluate

Explanation / Answer

we know that they are 1 km away from them so total time they will take to reach 1 km =1/108=.00925 hours = .555 minutes =33.33 seconds

while time taken by the cops will be

s=ut +(1/2)a(t)^2=1000=(1/2)*2*t^2

this gives t^2=1000 and t=31.62sec <33.33 sec so cops will catch them

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