Question

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 particle is 4
• B. The acceleration of particle is 2a
• C. The particle is at origin at t = 0
• D. None of these

Answer 1

Answer: (B)

The acceleration of particle is 2a

Answer 2

$x = 4(t - 2) + a(t - 2)^{2}$

At $t = 0,x = - 8 + 4a = 4a - 8$

$v = \frac{dx}{dt} = 4 + 2a(t - 2)$

At $t = 0,\mspace{6mu}\mspace{6mu} v = 4 - 4a = 4(1 - a)$

But acceleration, $a = \frac{d^{2}x}{dt^{2}} = 2a$