Question

A body is moving in a straight line with uniform acceleration. It covers distance of $10m$ and $12m$ in third and fourth seconds respectively. Then the initial velocity in m/sec is:

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

The correct option is D $5$

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

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

For $n=3$ and $S_3$

$S_3=u+\frac{a}{2}(6-1)=10$

$10=u+\frac{5a}{2}$. . . . . . . . .(2)

For $n=4$ and $S_4=12m$

$S_4=u+\frac{a}{2}(8-1)$

$12=u+\frac{7a}{2}$. . . . . . . . .(3)

Subtract equation (3) by equation (2),

$12-10=(u+\frac{7a}{2})-(u+\frac{5a}{2})$

$a=2m/s^2$

From equation (2),

$10=u+\frac{5\times 2}{2}$

$10=u+5$

$u=5m/s$

The correct option is D.