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# How to derive an equation of motion by integration?

Asked by 28th February 2009, 9:53 AM

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 [1]

 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 [2]

Answered by Expert 3rd March 2009, 10:21 AM
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