Question

A car accelerates from rest at constant rate for first $ 10\,\,s $ and covers a distance $ x $ . It covers a distance $ y $ in next $ 10\,\,s $ at the same acceleration. Which of the following is true?

• A. $ x=3y $
• B. $ y=3x $
• C. $ x=y $
• D. $ y=2x $

Answer 1

Answer: (B)

From equation of motion, we have
$s=u t+\frac{1}{2} a t^{2}$
where $u$ is initial velocity, $t$ is time, $a$ is acceleration.
Since car accelerates from rest $u=0, t=10 s$
$\therefore s=0+\frac{1}{2} \times a \times(10)^{2}=50 a \ldots$ (i)
Also, $v=u+a t$
where, $v$ is final velocity.
$\therefore $ Velocity after $10 s$ is
$v=0+a \times 10 $
$v=10 a=10 \times \frac{s}{50} \ldots$ (ii)
In the next $10\, s$ car moves with constant acceleration and with initial velocity
$\therefore s^{\prime}=v t+\frac{1}{2} a t^{2}$
$=\frac{s}{50} \times 10 \times 10+\frac{1}{2} \times \frac{s}{50} \times 100=3 s$
Given, $s=x$ and $s' =y$
$\therefore y=3 x$