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JEE Main 20253 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Evening Shift
Subject
Physics
Chapter
Motion in One Dimension

JEE Main 2025 · 3 April · Evening Shift · Physics · Motion in One Dimension

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

A particle moves along the xx-axis and has its displacement xx varying with time tt according to the equation x=c0(t2−2)+c(t−2)2\mathrm{x}=\mathrm{c}_0\left(\mathrm{t}^2-2\right)+\mathrm{c}(\mathrm{t}-2)^2 where c0c_0 and cc are constants of appropriate dimensions. Then, which of the following statements is correct?

Options

  1. Athe acceleration of the particle is 2c02 \mathrm{c}_0
  2. Bthe acceleration of the particle is 2 c2\mathrm{~c}
  3. Cthe initial velocity of the particle is 4 c4\mathrm{~c}
  4. Dthe acceleration of the particle is $2\left(c+c_0\right)

Correct answer

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

Step-by-step solution

v=dxdt=2tC0+2C(t−2)a=dvdt=2C0+2C\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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