25. A particle starts its motion from rest under the action of a constant force. If the distance covered in first 10 seconds is S1 and that covered in the first 20 seconds is S2, then:

25. 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:

(a)  \(S_2 = 3 S_1\)

(b)  \(S_2 = 4 S_1\)

(c)  \(S_2 = S_1\)

(d)  \(S_2 = 2 S_1\)

Answer :  (b)  \(S_2 = 4 S_1\)

u = 0

F is constant , hence a is constant

\( s = ut + \frac{1}{2}at^2 \)

\( s_1 = \frac{1}{2}a10^2 \)

\( s_1 = \frac{1}{2}a100 \)

\( s_2 = \frac{1}{2}a20^2 \)

\( s_2 = \frac{1}{2}a400 \)

\( s_2 = 4 × \frac{1}{2}a100 \)

\( \rightarrow s_2 = 4 S_1 \)