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 (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?

Answer 1

(c) : As u = 0, v₁ = at, v₂ = 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 = (1/2) at₁². For the second it is proportional to t. Therefore it is a parabola after crossing x-axis again. Curve (c) satisfies this.