Derive the following equation of motion by graphical method \mathrm{v^2=u^2+2as} where the symbols have their usual meanings.

Answer:

Consider the velocity-time graph of a body as shown below:

The initial velocity is u at the point A which changes from A to B at a uniform rate in time t. Let v be the final velocity which is equal to BC in the graph. OC represents the time t. A perpendicular is drawn CB from point C and AD is drawn parallel to OC. BE is perpendicular from point B to OE. The area under OABC is the distance travelled s.

Distance travelled, s = area of trapezium OABC

OA + CB = u + v

OC = t

Therefore, \mathrm{v^2=u^2+2as}

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