Question

A body covers $10m$ in $2^{nd}$ second and $25m$ in $5^{th}$ second of its motion. If the motion is uniformly accelerated, how far will it go in the $7^{th}$ second?

• A. $25m$
• B. $35m$
• C. $40m$
• D. $50m$

Answer 1

The correct option is B $35m$

We know,
$S_n=u+\frac{a}{2}(2n-1)$
From $2^{nd}$ second,
$10=u+\frac{a}{2}\times 3------\left(1\right)$
From $5^{th}$ second,
$25=u+\frac{a}{2}\times 9------\left(2\right)$
Subtracting equation (1) from (2), we get
$15=\frac{a}{2}\times 6$
$a=5m/s^2$
Substituting the value of $a$ in equation (1) we get,
$u=2.5m/s$
For $7^{th}$ second,
$S_n=u+\frac{a}{2}(2n-1)$
$S_n=2.5+\frac{5}{2}(2\times 7-1)=35m$