A motorist drives along a straight road at a constant speedof 22.5 m/s. Just as

Question

A motorist drives along a straight road at a constant speedof 22.5 m/s. Just as shepasses a parked motorcycle police officer, the officer starts toaccelerate at4.00 m/s2 to overtake her.Assume that the officer maintains this acceleration. (a) Determine the time it takes the police officer to reach themotorist.

(b) Find the speed of the officer as he overtakes themotorist.

(c) Find the total displacement of the officer as he overtakes themotorist.

(a) Determine the time it takes the police officer to reach themotorist.

(b) Find the speed of the officer as he overtakes themotorist.

(c) Find the total displacement of the officer as he overtakes themotorist.

Explanation / Answer

a)
     For the motorist s = vt
     For the police officer s= 0.5at2
     Whenpolice officer reach the motorist               vt =0.5at2
               v= 0.5at
               t = 2v / a                      =2*22.5 / 4.0                     = 5.625 s

b) v = at        = 4.0 x 5.625        = 22.5 m/s
c) s = 0.5at2        = 0.5 *4.0 * 5.625* 5.625         = 63.28 m        = 0.5 *4.0 * 5.625* 5.625         = 63.28 m

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