Motion in a Straight Line - Result Question 17
17. A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is $S_1$ and that covered in the first 20 seconds is $S_2$, then:
[2009]
(a) $S_2=3 S_1$
(c) $S_2=S_1$
(b) $S_2=4 S_1$
(d) $S_2=2 S_1$
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Answer:
Correct Answer: 17. (b)
Solution:
- (b) $u=0, t_1=10 s, t_2=20 s$
Using the relation, $S=u t+\frac{1}{2} a t^{2}$
Acceleration being the same in two cases,
$ \begin{aligned} & S_1=\frac{1}{2} a \times t_1^{2}, S_2=\frac{1}{2} a \times t_2^{2} \\ & \therefore \quad \frac{S_1}{S_2}=(\frac{t_1}{t_2})^{2}=(\frac{10}{20})^{2}=\frac{1}{4} \\ & \quad S_2=4 S_1 \end{aligned} $
