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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

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B

from rest and moves with uniform acceleration

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C

with an initial velocity and moves with uniform acceleration

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D

with an initial velocity and moves with uniform velocity

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Solution

## The correct option is C with an initial velocity and moves with uniform accelerationGiven:A body covers 26 meters in 10th secondA body covers 28 meters in 11th secondsA body covers 30 meters in 12th secondsA body covers 32 meters in 13th secondWe 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, $28-\frac{21×2}{2}=\mathrm{u}\phantom{\rule{0ex}{0ex}}\mathrm{u}=7\mathrm{m}/\mathrm{s}$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.

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