Question 116 of 308

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 $\mathrm{x}_1(\mathrm{t})$ after time ' $\mathrm{t}$ ' and that of the second body by $x_2(t)$ after the same time interval. Which of the following graphs correctly describes $\left(x_1-x_2\right)$ as a function of time ' $t$ '?

ABCD

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Answer: (B)

$$\begin{aligned} & x_1(t)=\frac{1}{2} a t^2 \\ & x_2(t)=v t \\ & x_1-x_2=\frac{1}{2} a t^2-v t \end{aligned}$$