First slide

Position time graph for positive negative zero acc

Question

A body starts moving unidirectionally under the influence of a source of constant power. Which one of the graph correctly shows the variation of displacement (s) with time (t)?

Difficult

Solution

P = Constant
$F V = m \frac{d V}{d t} V = k$
$\begin{array}{l} \int_{0}^{V} V d V = \frac{k}{m} \int_{0}^{t} d t \\ {[\frac{V^{2}}{2}]}_{0}^{V} = \frac{k}{m} {[t]}_{0}^{t} \\ \frac{V^{2}}{2} = \frac{k t}{m} \\ V = C \sqrt{t} \\ \frac{d s}{d t} = C \sqrt{t} \\ \int_{0}^{s} d s = C \int_{0}^{t} \sqrt{t} d t \\ S = C \frac{t^{3 / 2}}{3 / 2} \\ S = C_{1} \sqrt{t^{3}} \end{array}$
Not a straight line.

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