Question

A body travels for $15$ second starting from rest with constant acceleration . If it covers distances $S_1,S_2$ and $S_3$ in the first five seconds, second five seconds and next five seconds respectively then the relation between $S_1,S_2$ and $S_3$ is

• A. $S_1=S_2=S_3$
• B. $5S_1=3S_2=S_3$
• C. $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$
• D. $S_1=\frac{1}{5}{S}_2=\frac{1}{3}{S}_3$

Answer 1

The correct option is C $S_1=\frac{1}{3}{S}_2=\frac{1}{5}{S}_3$

Let ‘v’ denotes speed and ‘a’ denotes acceleration.

At t=0, v0= 0

At t=5, v5= 5a

At t=10, v10= 10a

For interval-1, (t=0 to t=5)

S1=v0*5 + (1/2)*a*52= 12.5a

For interval-2, (t=5 to t=10)

S2= v5*5 + (1/2)*a*52= 37.5a

For interval-3, (t=10 to t=15)

S3= v10*5 + (1/2)*a*52= 62.5a

Therefore, S1: S2: S3= 1:3:5