Question

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

• A. 80
• B. 50
• C. 20
• D. 30

Answer 1

Answer: (B)

The distance travelled in $n ^{\text {th }}$ second is
$S _{ n }= u +\frac{1}{2}(2 n -1) a \,\,\,... (1)$
So distance travelled in $t^{ \text{th} } \,\&\,(t+1)^{ \text{th }}$ second are
$S _{ t }= u +\frac{1}{2}(2 t -1) a \,\,\,... (2)$
$S _{ t +1}= u +\frac{1}{2}(2 t +1) a \,\,\,... (3)$
As per question,
$S _{ t }+ S _{ t +1}=100=2( u + at ) \,\,\,... (4)$
Now from first equation of motion the velocity of particle after time $t$,
if it moves with an acceleration $a$ is
$v = u + at \,\,\,... (5)$
where $u$ is initial velocity
So from equation (4) and (5),
we get $v =50\, cm / s$