Question

A particle moves along $x-axis$. The position $x$of particle with respect to time t from origin given by $x=b_0+b_{1}t+b_2{t}^2$. The acceleration of particle is

• A. $b_0$
• B. $b_1$
• C. $b_2$
• D. $2b_2$

Answer 1

The correct option is D

$2b_2$

Step1:Given data:

Time taken to cover distance along $x-axis=t$

Distance covered by the particle, $x=b_0+b_{1}t+b_2{t}^2$

Step2: Finding the acceleration of the particle.

We know that,

$v=\frac{dx}{dt}$

$\Rightarrow$$v=\frac{d\left(b_0+b_{1}t+b_2{t}^2\right)}{dt}$

$\Rightarrow$$v=b_1+2b_{2}t$ …….$\left(i\right)$

Where $v$ is the velocity of the particle and $\frac{dx}{dt}$ is change in distance with respect to time.

$a=\frac{dv}{dt}$

Where $a$ is the acceleration of the particle and $\frac{dv}{dt}$ is change in velocity with respect to time.

Now,

$a=\frac{d\left(b_1+2b_{2}t\right)}{dt}$ $\left[\because Fromequation\left(i\right)\right]$

$\Rightarrow$$a=2b_2$

Hence, option D is correct.