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How to derive an equation of motion by integration?
Asked by | 28 Feb, 2009, 09:53: AM Expert Answer

For first equation of motion, the definition of acceleration can be used.

For second equation of motion you can find the area under the v-t graph to find the distance covered by the body. For this integration can be used.

 a = dv dt dv = a dt v Δt ⌠ ⌡ dv = ⌠ ⌡ a dt v0 0 v − v0 = aΔt v = v0 + aΔt 

 v = dx dt dx = v dt x Δt Δt ⌠ ⌡ dx = ⌠ ⌡ v dt = ⌠ ⌡ (v0 + aΔt)dt x0 0 0 x − x0 = v0Δt + ½ aΔt2 x = x0 + v0Δt + ½ aΔt2 

Answered by | 03 Mar, 2009, 10:21: AM

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