Question

The velocity of a particle at an instant is $15\, ms ^{-1}$. After $5\, s$, its velocity will become $25\, ms ^{-1}$. The velocity at $4\, s$, before the given instant will be

• A. $23\, ms ^{-1}$
• B. $7 \, ms ^{-1}$
• C. $25\, ms ^{-1}$
• D. $15 \, ms ^{-1}$

Answer 1

Answer: (B)

Given, $u=15\, ms ^{-1}, t=5\, s$ and $v=25\, ms ^{-1}$
As, $v=u+a t$ .... (i)
where, $v$ is final velocity, $u$ is initial velocity, $a$ is acceleration and $t$ is time.
From Eq. (i) $\quad a=\frac{v-u}{t}$
Substituting given values of $v, u$ and $t$, we get
$a=\frac{25-15}{5}=\frac{10}{5}=2\, ms ^{-2}$
Now, velocity at $4 \,s$, before the given instant is given as
$v =u+a t $
where, $ v=15 \,ms ^{-1} , a=2 \,ms ^{-2} $ and $ t=4 \,s$.
$\Rightarrow 15=u+(2)(4) $
$\Rightarrow u=7 \,ms ^{-1}$