How to derive an equation of motion by integration?
Asked by | 28th Feb, 2009, 09:53: 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 | 3rd Mar, 2009, 10:21: AM
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