Question

A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate 2 f to come to rest. If the total diSstance travelled is 15 S, then S=?

Answer 1

Answer:

If t1 be the time for which the car accelerates at the rate f from rest, the distance traveled in time t1 is 

s=s1=0(t1)+21ft12=21ft12 ....(1) (using formula 

s=ut+21at2)

and the velocity at time t1 is v1=ft1

So, the distance traveled in time t will be s2=v1t=ft1t ...(2)

If t2 be the time for which the car decelerates at the rate f/2 to come rest, the distance traveled in time t2 is given by,

02−v12=2(−f/2)s3   (using formula v2−u2=2as) 

or s3=(ft1)2/f=ft12 ...(3)

using (1),  s