A speeder traveling at a constant speed of 132 km/h races past a billboard. A pa

Question

A speeder traveling at a constant speed of 132 km/h races past a billboard. A patrol car pursues from rest with constant acceleration of (8.4 km/h)/s until it reaches its maximum speed of 186 km/h, which it maintains until it catches up with the speeder.

(a) How long does it take the patrol car to catch the speeder if it starts moving just as the speeder passes? (in s)

(b) How far does each car travel? (in km)


A train pulls away from a station with a constant acceleration of 0.36 m/s2. A passenger arrives at a point next to the track 6.7 s after the end of the train has passed the very same point. What is the slowest constant speed at which she can run and still catch the train? (in m/s)

Explanation / Answer

The speeder speed v= 132km/h = 36.67m/s The acceleration of the patrol a = 8.4km/h/s = 2.33m/s^2 The maximum speed vmax = 186 km/h = 51.67m/s Let the speeder traveled distance x in time t x= vt The time taken to reach the maximum speed 51.67m/s = 2.33 t t = 51.67 / 2.33 = 22.2 sec The distance traveled in this time d = 0.5 (2.33)(22.2)^2 = 574m At this time the speeder at = (36.67)(22.2) = 814m Then if the both are meet at a distance d' from d d = 51.67 t' and d - 240 = 36.67 t' 51.67t' -240 = 36.67t' 15t' = 240 t' = 16s then the total time t = 22.2s + 16s = 38.2s The distance traveled d = 36.67*38.2 = 1400.76 m or 1.4km

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