Question:
How to derive second equation of motion by integration
Answer:
Velocity is the first derivative of displacement with respect to time. Reverse the operation in the definition. Instead of differentiating displacement to find velocity, integrate velocity to find displacement. This gives us the displacement–time equation for constant acceleration, also known as the second equation of motion.
| v = | dx | ||||
| dt | |||||
| dx = | v dt = (v0 + at) dt | ||||
| x | Δt | ||||
| ⌠⌡ |
dx = | ⌠⌡ |
(v0 + at) dt | ||
| x0 | 0 | ||||
| x − x0 = | v0Δt + ½aΔt2 | ||||
| x = | x0 + v0Δt + ½aΔt2 | ||||
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