Question

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 $x_1\left(t\right)$ after time $t$ and that of the second body by $x_2\left(t\right)$ after the same time interval. Which of the following graphs correctly describes $(x_1-x_2)$ as a function of time $t$?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

As $u=0,v_1=at,v_2=\text{constant}$ for the other particle. Initially both are zero. Relative velocity of particle 1 w.r.t. 2 is velocity of 1 - velocity of 2. At first the velocity of first particle is less than that of 2. Then the distance travelled by particle 1 increases as
$x_1=\left(1/2\right)a{t}_1^2$. For the second it is proportional to $t$. Therefore it is a parabola after crossing x-axis again. Curve (c) satisfy this.