Question

Two cars start off to a race with velocity $4m/s$ and $2m/s$ & travel straight line with uniform acceleration $1m/s^2$ and $2m/s^2$ respectively. If they reach the final point at the same instant, then the length of the path is :

• A. $30m$
• B. $32m$
• C. $20m$
• D. $24m$

Answer 1

Answer: (D)

$24m$

Let the length of the path is $s$

Now, $s=4t+\frac{1}{2}.1.t^2=2t+\frac{1}{2}.2.t^2$

$or,4t+0.5t^2=2t+t^2$

$or,\frac{t^2}{2}=2t$

$or,t=0and4$

Now. $t=0$ denotes the starting time. Hence for the final instance we take $t=4s$

So, $s=(2.4+\frac{1}{2}.2{.4}^2)m=24m$