Q. A particle moves along $x$-axis as $x = 4(t - 2) + a(t - 2)^{2}$ Which of the following is true
A) The initial velocity of the particle is 4
B) The acceleration of particle is $2a$
C) The particle is at origin at$t = 0$
D) None of these
Explanation
(b) $x = 4(t - 2) + a(t - 2)^{2}$
At $t = 0,\ x = - 8 + 4a = 4a - 8$
$v = \frac{dx}{dt} = 4 + 2a(t - 2)$
At $t = 0,\ v = 4 - 4a = 4(1 - a)$
But acceleration, $a = \frac{d^{2}x}{dt^{2}} = 2a$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.