Question

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

• A. $20$
• B. $30$
• C. $50$
• D. $80$

Answer 1

The correct option is C $50$

Sum of distance travelled in $t^{th}$ and $(t+1{)}^{th}$ second is $100\text{cm}$.
As we know that the distance travelled in $t^{th}$ second is given as,
$s_t=u+\frac{a}{2}(2t-1)$
$100=s_t+s_{t+1}$
$100=u+\frac{f}{2}(2t-1)+u+\frac{f}{2}\left[2\right(t+1)-1]$
$100=2u+\frac{f}{2}(2t-1+2t+2-1)$
$100=2u+\frac{f}{2}\left(4t\right)\Rightarrow 2u+2ft=100$
$50=u+ft$
On comparing with first equation of motion, $v=50\text{cm/s}$