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

MCQ

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 $( t +1)^{ th }$ seconds is $100 cm$, then its velocity after $t$ seconds, in $.........cm / s$, is

A
$80$
✓
$50$
C
$20$
D
$30$

✓

Answer

Correct option: B.

$50$

b
(b)

Sum of distance travelled in $t^{t h}$ and $(t+1)^{t h}$ seconds is $100 cm$

$u+\frac{a}{2}(2 t-1)+u+\frac{a}{2}(2(t+1)-1)=100$

$2 u+2 a t=100$

$u+a t=100 / 2$

$\Rightarrow v=50 cm / s$

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