Question

A particle moving in a straight line with initial velocity $u$ 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. $20$
• B. $30$
• C. $50$
• D. $80$

Answer 1

The correct option is C $50$

Solution 2

Distance travelled is $t^{th}sec=S\left(t\right)-S(t-1)$
Distance travelled is $(t+1{)}^{th}sec=S(t+1)-S(t)$
$S\left(t\right)-S(t-1)+S(t+1)-S\left(t\right)=100$
$S(t+1)=u(t+1)+\frac{1}{2}a(t+1{)}^2$
$S(t-1)=u(t-1)+\frac{1}{2}s(t-1{)}^2$
$S(t+1)+S(t-1)=$
$\Rightarrow 2(u+at)=100$
$u+at=50$