Question

A particle starts its motion from rest under the action of a constant force. If the distance covered in the first $10$ seconds is $S_{1}$ and that covered in the first $20$ seconds is $S_{2}$ , then:

• A. $S_{2} \, = \, 3 S_{1}$
• B. $S_{2} \, = \, 4 S_{1}$
• C. $S_{2} \, = \, S_{1}$
• D. $S_{2} \, = \, 2 S_{1}$

Answer 1

Answer: (B)

Given:
$u \, = \, 0 \, , \, t_{1} \, = \, 10 s \, , \, t_{2} \, = \, 20 s$
Using the relation, $S \, = \, u t + \frac{1}{2} a t^{2}$
Acceleration being the same in two cases.
$S_{1} \, = \, \frac{1}{2} \, a \, \times \, t_{1}^{2} \, , \, S_{2} \, = \, \frac{1}{2} \, a \, \times \, t_{2}^{2}$
$\therefore \, \frac{S_{1}}{S_{2}} \, = \, \left(\right. \frac{t_{1}}{t_{2}} \left.\right)^{2} \, = \, \left(\right. \frac{10}{20} \left.\right)^{2} \, = \, \frac{1}{4}$
$S_{2} \, = \, 4 S_{1}$