A motorist traveling with a constant speed of 25.0 m/s passes a school-crossing

Question

A motorist traveling with a constant speed of 25.0 m/s passes a school-crossing corner, whereas speed limit is 20 m/s Just as the motorist passes the school crossing sign, a police officer on a motorcycle stopped there starts in pursuit with a constant acceleration of 5.0 m/s^2. (a) How much time elapses before the officer passes the motorist? (b) what is the Officer's speed at the time? (c) at the time, what distance has each vehicle travels? v = V_0 + at v^2 = V^2_0 + 2ax x = x_0 + v_0 t + 1/2 at^2 v = 1/2(v^0 = V^f)(5)x = vt

Explanation / Answer

(A) suppose officer catches in time t.

in this time, dstance travels by both will be same.

by the motorist,

d1 = 25t

by the officer,

d3 = u t + a t^2 /2 = 0 + 5 t^2 /2 = 2.5 t^2

so d1 = d3

25t = 2.5 t^2

t = 25/2.5 = 10 sec

(B) v = u + a t

v =0 + 5 x 10 = 50 m/s

(C) d = 25t = 250 m

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