Question

A body covers 20 m, 22 m, 24 m, in $8^{th},9^{th}$ and ${10}^{th}$ seconds respectively. The body starts

• A. from rest and moves with uniform velocity.
• B. from rest and moves with uniform acceleration.
• C. with an initial velocity and moves with uniform acceleration.
• D. with an initial velocity and moves with uniform velocity.

Answer 1

The correct option is C with an initial velocity and moves with uniform acceleration.

The distance covered by the particle in $n^{th}$ second,

$S_n=u+\frac{a}{2}(2n-1)$

$S_8=20m$

$S_8=u+\frac{a}{2}(2\times 8-1)$

$20=u+7.5a$. . . . . . . . .(1)

$S_9=22=u+\frac{a}{2}(2\times 9-1)$

$22=u+8.5a$. . . . . . . .(2)

By solving equation equation (1) and (2), we get

$u=5m/s$ , $a=2m/s^2$

Now, $S_{10}=u+\frac{a}{2}(2\times 10-1)$

$S_{10}=5+\frac{1}{2}\times 2(2\times 10-1)$

$S_{10}=5+19=24m$

Hence, body starts with the initial velocity and moves with uniform acceleration.

The correct option is C.