A particle is moving in a straight line with initial velocity u a… - Vidyadip

MCQ

A particle is moving in a straight line with initial velocity $u$ and uniform acceleration a. If the sum of the distances travelled in $t^{\text {th }}$ and $(t+1)^{\text {th }}$ seconds is $100\ cm , $then its velocity after $t$ seconds in $cm s ^{-1}$ is

✓
$50$
B
$80$
C
$30$
D
$20$

✓

Answer

Correct option: A.

$50$

Distance travelled in $t ^{\text {th }}$ second of uniformly accelerated motion is $S_{t}=u+\frac{a}{2}(2 t-1) \ldots(i)$
Distance travelled in $(t+1)^{\text {th }}$ second can be written as $S_{t+1}=u+\frac{a}{2}[2(t+1)-1]$
$\text { or } S_{t+1}=u+\frac{a}{2}(2 t+1) \ldots \text { (ii) }$
$s_{t}+s_{t+1}=100 \ cm($ given $)$
$u+\frac{a}{2}(2 t-1)+u+\frac{a}{2}(2 t+1)=100[$ Using $(i)$ and $(ii)]$
or $2 u+2 at=100$ or $u+at=50$
$\therefore v=50 \ cms^{-1}$

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