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 theposted speed limit. A policeman waits 7.0 s before giving chase atan acceleration of 3.0m/s2. (a) Find the time required to catch the car from the instantthe car passes the policeman.
-------------------- s (b) Find the distance required for the policeman to overtakethe motorist. ------------------ m A motorist travels at a constant speed of 35.5 m/s through a school zone, exceeding theposted speed limit. A policeman waits 7.0 s before giving chase atan acceleration of 3.0m/s2. (a) Find the time required to catch the car from the instantthe car passes the policeman.
-------------------- s (b) Find the distance required for the policeman to overtakethe motorist. ------------------ m

Explanation / Answer

Let the time required to catch the car from the instant thecar passes the policeman be t Distance travel by motorist in the time ( t )s   is   S = Velocity / time                                                                                   = ( 35.5 m / s )  * ( t ) Distance travel by police in time t is S = ut + (1/ 2 ) a t ^ 2                                                            =( 1/ 2) a ( t-7 ) ^ 2    Since initialvelocity u = 0                                                                                                       time t = t - 7                                                           = ( 1/ 2) 3 ( t-7 ) ^ 2                                                           = 1.5 ( t - 7 ) ^ 2 from the problems , 1.5 ( t - 7 ) ^ 2 = 35.5 *t                                      ( t-7 ) ^ 2 = 23.666 t                        [ t ^ 2 -14 t + 49 ] = 23.666 t                           t ^ 2 - 37.666 t + 49 = 0 t = 37.666 ± [ (-37.666) ^ 2 - 4(1) ( 49) ] / 2     = ( 37.666 ± 34.96 ) /2     = 36.31 s   or 1.353 s If t = 1.353 then t-7 is negative.So, answeris t = 36.31 s (b). The distance required for the policeman to overtakethe motorist S = 1.5 ( 36.31 -7 ) ^ 2                                                                                                            = 1288.61 m                                                                                                            ~ 1290 m

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