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 $a$.
• C. the acceleration of the particle is $2a$.
• D. at $t=2s$ particle is at the origin.

Answer 1

Answer: (C), (D)

The correct options are
C the acceleration of the particle is $2a$.
D at $t=2s$ particle is at the origin.

We can write the equation as,
$X=u(t-2)+\frac{1}{2}\left(2a\right){(t-2)}^2$
clearly, $X=0$ at $t=2$
Also, acceleration$=2a$ when we compare the given equation with
$X=ut+\frac{1}{2}a{t}^2$