Question

A body covers $26$ and $28$ meters in ${10}^{th}$ and ${11}^{th}$ 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.

Distance covered by a body in $n^{th}$ second is given by
$s_{n^{th}}=u+\frac{a}{2}(2n-1)$
$\Rightarrow s_{{10}^{th}}=u+\frac{a}{2}(2\times 10-1)$
$\Rightarrow 26=u+\frac{19a}{2}$......(i)
Similarly, $s_{{11}^{th}}=u+\frac{a}{2}(2\times 11-1)$
$\Rightarrow 28=u+\frac{21a}{2}$.......(ii)
On solving (i) & (ii), we get
$u=7\text{m/s},a=2{\text{m/s}}^2$
Hence, the body starts with initial velocity and moves with uniform acceleration.