A motorist travels at a constant speed of 35.5 m/s through a school zone, exceed

Question

A motorist travels at a constant speed of 35.5 m/s through a school zone, exceeding the posted speed limit. A policeman waits 7.0 s before giving chase at an acceleration of 3.3 m/s^2. Find the time required to catch the car from the instant the car passes the policeman. Write the equations for the position of the speeder at time t and for the position of the policeman who starts 7.0 seconds later. Find the time when the two meet. Find the distance required for the policeman to overtake the motorist. This is the answer that would result from your result for part (a), but because your answer for part (a) was wrong your answer here is also wrong.

Explanation / Answer

speed of motorist ,Vm= 35.5 m/s

acceleration of policeman ,a = 3.3 m/s2

let the police goes for time = t

time travelled by motorist = t+7 ( since for 7 sec policeman wait)

distance travelled by motorist, dm = speed*time

dm = 35.5 * ( t+7)

distance travelled by police, dp :[ here u = initail velocity of police = 0]

from S = u*t + ( 1/2)*a*t2

   dp = 0+ ( 1/2)*3.3*t2

police will catch the car when dm = dp

  35.5 * ( t+7) =  ( 1/2)*3.3*t2

71 t + 497 = 3.3t2

on solving this equation, t = 27.07 s

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b) distance required by policeman to overtake the motorist

distance = 35.5 * ( t+7)

= 35.5*(27.07 +7)

= 1209.4m

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