Question

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

• A. 80
• B. 50
• C. 20
• D. 30

Answer 1

The correct option is B 50

The distance travelled in $n^{th}$ second is
$S_n=u+\frac{1}{2}(2n-1)a$ ....(1)
So distance travelled in $t^{th}\&{(t+1)}^{th}$ second are
$S_t=u+\frac{1}{2}(2t-1)a$ ....(2)
$S_{t+1}=u+\frac{1}{2}(2t+1)a$ ....(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 $v=50cm/s$