Question

Two scooters starting from rest accelerate uniformly at the same rate. The second travels for twice the time of the first. 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

$s_2=4s_1$

$s=ut+\frac{1}{2}a{t}^2,u=0.$
$\Rightarrow s=\frac{1}{2}a{t}^2$
Since, ${}^{\prime }{a}^{\prime }$ is constant, $s\propto t^2$
$\Rightarrow \frac{s_1}{s_2}=\frac{t_1^2}{t_2^2}\Rightarrow \frac{s_1}{s_2}=\frac{t_1^2}{\left(4t_1^2\right)}\Rightarrow s_2=4s_1.$