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A particle moves along the x-axis and has its displacement x varying with time t according to the equation x=c0 (t^2-2 )+c(t-2)^2 where c0 and c are constants of appropriate dimensions. Then, which of the following statements is correct?

the acceleration of the particle is 2 (c+c0 )

the acceleration of the particle is 2 c0

the acceleration of the particle is 2~c

the initial velocity of the particle is 4~c

Kinematics

JEE Main level, single correct, medium

122 of 308

Question 122 of 308

A particle moves along the $x$ -axis and has its displacement $x$ varying with time $t$ according to the equation $\mathrm{x}=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2$ where $c_0$ and $c$ are constants of appropriate dimensions. Then, which of the following statements is correct?

Show answer and solution

Answer: (D) the acceleration of the particle is $2\left(c+c_0\right)$

\begin{aligned} & \mathrm{v}=\frac{\mathrm{dx}}{\mathrm{dt}}=2 \mathrm{tC}_0+2 \mathrm{C}(\mathrm{t}-2) \\ & \mathrm{a}=\frac{\mathrm{dv}}{\mathrm{dt}}=2 \mathrm{C}_0+2 \mathrm{C}\end{aligned}

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JEE Main 2025 Apr 2 Shift 1 question paper

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