Question

Two scooters starting from rest accelerate uniformly at the same rate. The time taken by the second scooter ($s_2$) to travel is twice the time taken by the first scooter ($s_1$). What is the relation between the distance covered by $s_1$ to that of $s_2$?

• 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 $s_2=4s_1$

The second equation of motion is given as:
$s=ut+\frac{1}{2}a{t}^2$
However, u = 0 since both scooters start from rest.
Therefore, $s=\frac{1}{2}a{t}^2$
Since a is constant,
$s\alpha t^2$
$s_1$ is the distance covered by the first scooter in time $t_1$.
$s_2$ is the distance covered by the second scooter in time $t_2$.
According to the question,
$t_2=2t_1$
$\frac{s_1}{s_2}=\frac{t_1^2}{t_2^2}$
$\frac{s_1}{s_2}=\frac{t_1^2}{4t_1^2}$
$s_2=4s_1$