JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Kinematics

A particle moves along the x-axis and has its displacement

x

varying with time

t

according to the equation

x = c_{0} (t^{2} - 2) + c (t - 2)^{2}

where

c_{0}

and c are constants of appropriate dimensions. Then, which of the following statements is correct?

(A)the acceleration of the particle is $2 c_{0}$
(B)the acceleration of the particle is 2c
(C)the initial velocity of the particle is 4c
(D)the acceleration of the particle is $2 (c + c_{0})$ ✓ Correct

Answer: (D)

Solution

The velocity is the first time derivative,

v = \frac{d x}{d t} = 2 c_{0} t + 2 c (t - 2)

. Differentiating once more, the acceleration is

a = \frac{d v}{d t} = 2 c_{0} + 2 c

, constant in time. The acceleration of the particle is

2 (c + c_{0})

JEE Main · 2025 · 03 Apr 2025 · Shift 2 · Single correct option

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