A motorist drives along a straight road at a constant speed of 15.0m/s. Just as
ID: 1662241 • Letter: A
Question
A motorist drives along a straight road at a constant speed of 15.0m/s. Just as she passes a parked motorcycle police officer,the officer starts to accelerate at 2.00m/s2. Assuming the officer maintains this acceleration,(a) determine the time it takes the police officer to reachthe motorist. (b) Find the speed of the officer as they overtake themotorist. (c) Find the total displacement of the officer as theyovertake the motorist.
Thanks in advance; will rate soon.
(a) determine the time it takes the police officer to reachthe motorist. (b) Find the speed of the officer as they overtake themotorist. (c) Find the total displacement of the officer as theyovertake the motorist.
Thanks in advance; will rate soon.
Explanation / Answer
Constant Velocityof motorist, V1 = 15 m/s Initialvelocity of pokice officer, V2 = 0 m/s Accelerationof the police officer, a = 2 m/s^2 ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (a) Time taken by the police officer to meet motorist = t Distance traveled by the police officer = Distance traveled by the motorist V2 t + ( 1/2 ) a t 2 = V1 t 0.5 * 2 t 2 = 15 t t 2 = 15 t Time taken to meet the police officer, t = 15 s ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (b) Speed of the police officer when overtaking motorist = V2 + a t = 0 + 2 * 15 = 30 m/s ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ (c) Displacement of the officer = V2 t + ( 1/2 ) a t 2 = 0 + 0.5 * 2 * 15 2 = 225 m
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