Question

A body covers 26, 28, 30, 32 meters in 10th, 11th, 12th and 13th 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

Given:

1. A body covers 26 meters in 10^th second
2. A body covers 28 meters in 11^th seconds
3. A body covers 30 meters in 12^th seconds
4. A body covers 32 meters in 13^th second

We know the formula of the distance covered in nth second is
${\mathrm{s}}_{\mathrm{n}}=\mathrm{u}+\frac{1}{2}\left(2\mathrm{n}-1\right)\mathrm{a}$

(here, s= distance , u = initial velocity ,n = the nth second , a = acceleration)

Using the above formula,

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

Similarly,

$28=\mathrm{u}+\frac{21\mathrm{a}}{2}...........\left(2\right)$
$30=\mathrm{u}+\frac{23\mathrm{a}}{2}...........\left(3\right)$
$32=\mathrm{u}+\frac{25\mathrm{a}}{2}...........\left(4\right)$

From equations (1) and (3) we get,

$26-\frac{19\mathrm{a}}{2}=\mathrm{u}$ and $28-\frac{21\mathrm{a}}{2}=\mathrm{u}$

$26-\frac{19\mathrm{a}}{2}=28-\frac{21a}{2}$

$\mathrm{a}=2{\mathrm{ms}}^{-2}$

And,

$$\begin{gathered} 28-\frac{21\times 2}{2}=\mathrm{u} \\ \mathrm{u}=7\mathrm{m}/\mathrm{s} \end{gathered}$$

Therefore the body starts with an initial velocity of $\mathrm{u}=7{\mathrm{ms}}^{-1}$and with a uniform acceleration of $2{\mathrm{ms}}^{-2}$

Hence, the correct option is C.