A motorist drives along a straight road at a constant speed of15.0 m/s. Just as

Question

A motorist drives along a straight road at a constant speed of15.0 m/s. Just as she passes a parkedmotorcycle police officer, the officer starts to accelerate at1.50 m/s2 to overtake her.Assume that the officer maintains this acceleration. (a) Determine the time it takes the policeofficer to reach the motorist. s
(b) Find the speed of the officer as he overtakes themotorist. m/s
(c) Find the total displacement of the officer as he overtakes themotorist. m (a) Determine the time it takes the policeofficer to reach the motorist. s
(b) Find the speed of the officer as he overtakes themotorist. m/s
(c) Find the total displacement of the officer as he overtakes themotorist. m

Explanation / Answer

a) let the time be t. for police: distance d1 = (1/2)at2 =0.5*1.50m/s2*t2 for the motorist, distance d2 = vt=15.0m/s*t when the police overtake the motorist, we have: d1= d2 => 0.5*1.50m/s2*t2 = 15.0m/s *t => t = 15.0m/s / 0.5*1.50m/s2 = 20 s b) the speed of the police v is: v= at = 1.50m/s2 * 20 s = 30.0 m/s c) d1 = 0.5*1.50m/s2*t2 = 300m total displacement of the officer is 300 m => 0.5*1.50m/s2*t2 = 15.0m/s *t => t = 15.0m/s / 0.5*1.50m/s2 = 20 s b) the speed of the police v is: v= at = 1.50m/s2 * 20 s = 30.0 m/s c) d1 = 0.5*1.50m/s2*t2 = 300m total displacement of the officer is 300 m

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