Question

Two scooters starting from rest accelerate uniformly at the same rate. Time taken by second scooter to travel is twice the time taken by the first scooter. Then the relation between the distance covered by the first scooter $\left(S_1\right)$ to that of the second scooter $\left(S_2\right)$ is

• A. $S_1=S_2$
• B. $S_1=2S_2$
• C. $S_2=3S_1$
• D. $S_2=4S_1$

Answer 1

The correct option is D $S_2=4S_1$

Let u be the initial velocity, t be the time taken, a is the acceleration and S is the distance covered.
Using the second equation of motion
$S=ut+\frac{1}{2}a{t}^2$,
$(u=0$ since it starts from rest).
$\Rightarrow S=\frac{1}{2}a{t}^2$
Since, 'a' is constant, $S\propto t^2$
Let $S_1$ be the distance covered by the first scooter and $S_2$ be the distance covered by the second scooter.
Let $t_1$ be the time taken by the first scooter and $t_2$ be the time taken by the second scooter.
According to the question, $t_2$ = 2$t_1$
Then, $\frac{S_1}{S_2}=\frac{t_1^2}{t_2^2}$

or, $\frac{S_1}{S_2}=\frac{t_1^2}{\left(4t_1^2\right)}$

or, $S_2=4S_1$