Question

The velocity of a particle moving with constant acceleration at time $t_0$ is $10\text{m/s}$. After $5\text{second}$, velocity is $20\text{m/s}$. The velocity $3\text{sec}$ before time $t_0$ is

• A. $8\text{m/s}$
• B. $4\text{m/s}$
• C. $6\text{m/s}$
• D. $7\text{m/s}$

Answer 1

The correct option is B $4\text{m/s}$

Given:
$t_i=t_0;v_i=10\text{m/s}$
$t_f=(t_0+5)\text{s};v_f=20\text{m/s}$

Let $a$ be the constant acceleration of given motion.

As we know that,

$a=\frac{v_f-v_i}{t_f-t_i}=\frac{20-10}{(t_0+5-t_0)}=2{\text{m/s}}^2$

Let $v_b$ be the velocity of particle $3\text{s}$ before $t_0$.

Now applying first equation of motion,

$v=u+at$

here, $u=v_b;v=10\text{m/s};t=3\text{s}$

$\Rightarrow 10=v_b+(2\times 3)$

$\Rightarrow v_b=4\text{m/s}$

Hence, option $\left(b\right)$ is the correct answer.