Question

A body covers $26,28,30$ and $32$ meters in ${10}^{th}$, ${11}^{th},{12}^{th}$ and ${13}^{th}$ 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 in $n^{th}$ second is

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

where $u$ is initial velocity $\&a$ is acceleration

then, $26=u+\frac{19a}{2}.........\left(1\right)$

$28=u+\frac{21a}{2}..........\left(2\right)$

$30=u+\frac{23a}{2}..........\left(3\right)$

$32=u+\frac{25a}{2}............\left(4\right)$

From eqs.$\left(1\right)$and $\left(2\right)$ we get $u=7m/s,a=2m/s^2$

$\therefore$ The body starts with initial velocity $u=7m/s$ and moves with uniform acceleration $a=2m/s^2$