Q 11-02-140JEE MainJEE Main 2025 (3 Apr, Shift 2)Easy
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?
Answer: (D) the acceleration of the particle is $2(c + c_0)$
$$v = \frac{dx}{dt} = 2c_0t + 2c(t - 2),\qquad a = \frac{dv}{dt} = 2c_0 + 2c = 2(c + c_0)$$
(At $t = 0$ the velocity is $-4c$, so statement (3) is wrong.)
Solution by Sreeraj P, M.Sc Physics