CBSE Class 11-science Answered
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 | [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 | 03 Mar, 2009, 10:21: AM
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