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

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?
according to velocity time graph the total distance covered will be given by the area of the curve. let t be the time in which the car attains maxixmum speed. so applying the formula we will get the quadratic eq like 2.25t*t-367.2t+3840=0 solving this eq for t we will get the value of t as 11.18sec
so the time =11.18sec
(b) What distance did the car cover during the acceleration phase of its motion?
s=0+1/2*4.5*11.18*11.18
(c) What was the top speed reached by the car? v=0+4.5*11.18

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