A physics 109 student is taking a car for a joy ride on a long, empty and perfec

Question

A physics 109 student is taking a car for a joy ride on a long, empty and perfectly
straight Saskatchewan highway. At the beginning of the joy ride the student has the
car accelerate from rest to some top speed with a (constant) acceleration of 4:50 m=s2
and then maintains that top speed to the end of the ride. The total time taken from
the start of the joy ride to its end is 1:36 minutes and the total distance covered is
3:84 km.
(a) What was the time elapsed during the acceleration phase of the car's motion?
(b) What distance did the car cover during the acceleration phase of its motion?
(c) What was the top speed reached by the car?

Explanation / Answer

(c) in the total journey of car's motion initial velocity u = 0.0 m/s final velocity   v = ? the time taken t = 1.36 *60 s = 81.6 s total distance covered s = 3.84*10^3 m using kinematic relation S = ut + (1/2) *a t^2 3.84*10^3 m = (0.0) t + (1/2) *a *(81.6 s)^2 Average acceleration a = 1.153 m/s^2 The velocity v = u + a*t v = 0.0 + 1.153*81.6 The top speed reached by the car v = 94.08 m/s (b)during acceleration intinl velocity u = 0.0 m/s acceleration a = 4.5 m/s^2 final velocity v = 94.08 m/s The distance travelled during acceleration v^2 - u^2 = 2as s = 983.4 m (a) time taken v = u + at time taken during acceleration t = v/a = 94.08 m/s / 4.5 m/s^2 = 20.90 s

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