Question
Tue June 19, 2012 By: Ratik Mahajan

A car, starting from rest, accelerates at a rate 'f' through a distance 's', then continues at a constant speed for sometime 't' and then decelerates at the rate 'f/2' to come to rest. If the total distance is '5s', then prove that s=1/2ft^2 or s=1/2f(t)square

Expert Reply
Tue June 19, 2012

Initial speed =0

Thus using the third equation of motion we can find the final velocity after moving a distance s.

 

After that the car moved at a constant speed for t time we can calculate the distance travelled:

 

Now after that it is decelerated by f/2 so we can find the distance covered as:

 

Now total distance travelled is 5s

Thus

 

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