Question

The given graph shows the variation of velocity (v) with position (x) for a particle moving along a straight line

Which of the following graph shows the variation of acceleration (a) with position (x)?

Options

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Answer 1

Explanation:

The position of the velocity equation for the given graph is given as,

v = – mx + v₀

∴ v = `((-v_0)/x_0) x + v_0` ......(i)

∴ `(dv)/(dt) = ((-v_0)/(x_0)) (dx)/(dt) = ((-v_0)/(x_0))v`

Substituting equation (i), we get,

`(dv)/(dt) = ((- v_0)/(x_0)) [((- v_0)/(x_0))x + v_0]`

∴ a = `((v_0)/(x_0))^2 x - (v_0^2)/(x_0)`

As a result, the acceleration-position graph is a straight line with a positive slope and a negative intercept; that is, graph (A).