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

Question

A physics 109 student is taking car for a joy ride on a long, empty and perfectly straight Saskatchewan high way. At the beginning of the joy ride the student has the car accelerate from rest to some top speed with a (constant) acceleration of 4.50m/s^2 and then maintains that top speed to the end of the ride. The total time taken from the beginning of the joy ride to its end is 1.36 minutes and the total distance covered is 3.84km.
(a) What was the time elapse during the acceleration phase of the car's motion?
(b) What distance did the car cover during the acceleration phase of its motion?
(a) What was the top speed reached by the car?

Explanation / Answer

The acceleration of the car a = 4.50m/s^2 The total time taken to ride t = 1.36min = 1.36(60s) = 81.6s
The total distance traveled x = 3.84m Let the time taken to acceleration phase is t1 and the then the remaining time is t2 so the total time t = t1+t2 = 1.36min or 81.6s the velocity of the car after traveling a time t1    v = at1 then the total distance    x = (1/2)at1^2+ vt2
= (1/2)at1^2+ (at1) t2
= at1 [ 0.5t1 + t2] But t1 + t2 = 81.6s    so t2 = 81.6 - t1 then x= at1 [ 0.5t1 + 81.6-t1] = at1 [ -0.5t1 + 81.6 ]
   3.84 = (4.5)t1 [ - 0.5t1 + 81.6]
2.25t -367.2t1 + 3.84 =0
t1 = 163.2s the time elapsed during the acceleration phase of the car's motion
   t1 = 163.2s the time elapsed during the acceleration phase of the car's motion
   t1 = 163.2s The distance cover by car during the acceleration phase of its motion     x1 = (1/2)(4.5)(163.2)
= 367.2m
(c) The top speed reached by car
    x1 = (1/2)(4.5)(163.2)
= 367.2m
v = 4.5 (163.2) = 734.4 m/s

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