A body is at rest at x = 0. At t = 0, it starts moving in the… | JEE Main 2008 (AIEEE)

Q34JEE Main 2008 · AIEEEMedium

Graphs of Motion

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 $\text{'}t\text{'};$ 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 $\text{'}t\text{'}$ ?

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Answer: (b)

$x_1 = \frac{1}{2}at^2$ , $x_2 = ut$ , so $x_1 - x_2 = \frac{1}{2}at^2 - ut$ .
This is an upward parabola through the origin: negative for $0 < t < \frac{2u}{a}$ , zero at $t = \frac{2u}{a}$ , then positive and rising.
So the answer is (b).

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Graphs of Motion question from JEE Main 2008 (AIEEE)

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