A body is at rest at $x = 0$. At $t = 0$, it starts moving in the positive $x$-direction with a constant acceleration. At the same instant another body passes through $x = 0$ moving in the positive $x$-direction with a constant speed. The position of the first body is given by $x_{1}(t)$ after time ‘$t$’ and that of the second body by $x_{2}(t)$ after the same time interval. Which of the following graphs correctly describes $(x_{1} - x_{2})$ as a function of time ‘$t$’

Question

Dr. Abubacker · Accepted Answer

(a) $x_{1} = \frac{1}{2}at^{2}$ and $x_{2} = ut\ 	herefore x_{1} - x_{2} = \frac{1}{2}\ at^{2} - ut$
$y = \frac{1}{2}at^{2} - ut$.This equation is of parabola
$\frac{dy}{dt} = at - u$ and $\frac{d^{2}y}{dt^{2}} = a$
As $\frac{d^{2}y}{dt^{2}} > 0$ $i.e.,$ graph shows possess minima at $t = \frac{u}{a}$

Explanation

Reviewed by Dr. Abubacker

Want more practice?