A car traveling at a constant speed at 30m/s passes a trooper hidden behind a bi

Question

A car traveling at a constant speed at 30m/s passes a trooper hidden behind a billboard. When the speeding car passes the billboard, the trooper sets in chase at 3m/s^2. How long does it take the trooper to overtake the speeding car? Please show work as well.

Explanation / Answer

The distance traveled by the speeding car after being spotted will be 30*t. The distance traveled by the trooper after setting chase will be (1/2)*3*t^2. (Recall that distance d(t) = d(0) + v(0)*t + (1/2)*a*t^2.) The trooper will catch the speeder when 30t = (3/2)t^2. Excluding t=0 this means that 30 = (3/2)t ---> t = 20 seconds. For the second question, the best formula to use is (v(final))^2 = (v(initial))^2 + 2ad. In this case the final velocity will be 0, the initial velocity is 110 km/hr * (1000m/km) * (1 hr / 3600 s) = 30.556 m/s, and a = -300 m/s^2. What we want, of course, is d, which will be the minimum thickness of the barrier needed. So 0 = 30.556^2 + 2 * (-300) * d ---> d = 30.556^2 / 600 = 1.556 m.

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