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JEE Main 2025 (3 Apr, Shift 2) · Velocity, Acceleration & Variable Motion

Velocity, Acceleration & Variable Motion question from JEE Main 2025 (3 Apr, Shift 2)

Q3JEE Main 2025 · 3 APR · SHIFT 2Medium

Velocity, Acceleration & Variable Motion

A particle moves along the xx-axis and has its displacement xx varying with time t according to the equation:

x=c0(t2−2)+c(t−2)2x = c_0\left(t^2 - 2\right) + c(t - 2)^2

where c0c_0 and c are constants of appropriate dimensions.

Then, which of the following statements is correct?

Show answer and solution

Answer: (a)

  1. v=dxdt=2c0t+2c(t−2)v = \dfrac{dx}{dt} = 2c_0 t + 2c(t - 2)
  2. a=dvdt=2c0+2c=2(c+c0)a = \dfrac{dv}{dt} = 2c_0 + 2c = 2(c + c_0)
  3. Initial velocity v(0)=−4cv(0) = -4c, so (d) is wrong.
  4. So the answer is (a) 2(c+c0)2(c + c_0).
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