Question

A particle moves along $x-$ axis as $x=4\left(t-2\right)+a{\left(t-2\right)}^2$ , here $a$ is a constant. Which of the following is true?

• A. The initial velocity of the particle is $4m{s}^{-1}$
• B. The acceleration of particle is $2a$
• C. The particle is at origin at $t=0$
• D. None of the above

Answer 1

Answer: (B)

Given, $x=4\left(t-2\right)+a{\left(t-2\right)}^2$
$v=\frac{dx}{dt}=4+2a\left(t-2\right)$
At $t=0,v=4\left(1-a\right)\text{and }x=\left(4a-8\right)$
Acceleration, $a=\frac{d^{2}x}{d{t}^2}=2a$