Q 11-02-092JEE MainJEE Main 2022 (25 Jun, Shift 2)Medium
Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $x_P(t) = \alpha t + \beta t^2$ and $x_Q(t) = ft - t^2$. At what time do both the buses have the same velocity?
Answer: (D) $\dfrac{f - \alpha}{2(1+\beta)}$
$v_P = \dfrac{dx_P}{dt} = \alpha + 2\beta t$ and $v_Q = f - 2t$.
$$\alpha + 2\beta t = f - 2t\ \Rightarrow\ t = \frac{f-\alpha}{2(1+\beta)}$$
Solution by Sreeraj P, M.Sc Physics