Question

A particle moves along the $X-$axis as
$x=u(t-2)+a(t-2{)}^2$

• A. the initial velocity of the particle is $u$
• B. the acceleration of the particle is $\alpha$
• C. the acceleration of the particle is $2\alpha$
• D. at $t=2s$ particle is at the origin.

Answer 1

Answer: (A), (C), (D)

the acceleration of the particle is $2\alpha$
at $t=2s$ particle is at the origin.
the initial velocity of the particle is $u$

We know,

$v=\frac{dx}{dt}=u+2a(t-2)$ (1)

$a=\frac{d^{2}x}{d{t}^2}=2a$ (2)

Here we will discuss all the option,

$\text{Case 1}$

Initial velocity means, v at t=0,

i.e ,$v=u-4a\ne u$

Option $\text{A}$ is correct.

$\text{Case 2}$

It is clear from equation (1) that ,

Acceleration$=2a$

Option $\text{B}$ is incorrect and option $\text{C}$ is correct.

At t=2s,

$x=0$ i.e particle is ar origin.

Option $\text{D}$ is correct.