A particle moves along the X-axis as x = u(t - 2s) + a(t - 2s)^2. - Vidyadip

MCQ

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

A
The initial velocity of the particle is $u.$
B
The accelerati? $n $ of the particle is $a.$
✓
The acceleration of the particle is $2a.$
D
At $t = 2s$ particle is at the origin.

✓

Answer

Correct option: C.

The acceleration of the particle is $2a.$

Initial velocity $=\Big|\frac{\text{dx}}{\text{dt}}\Big|_{\text{t} = 0}$
$\frac{\text{dx}}{\text{dt}}=\text{u}+2\text{a}(\text{t}-2\text{s})$
$\Big|\frac{\text{dx}}{\text{dt}}\Big|_{\text{t}=0}=\text{u}-4\ \text{as}\neq\text{u}$
Acceleration $=\frac{\text{d}^2\text{x}}{\text{dt}^2}=2\text{a}$
At $t = 2s,$
$x = u(2s - 2s) + a(2s - 2s)^2 = 0 ($origin$)$

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