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

The Correct Option is B

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