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Motion: displacement, velocity and acceleration
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Learn it If s(t) is position, then velocity v(t) = s′(t) and acceleration a(t) = v′(t) = s″(t). The object is at rest when v = 0 and speeding up when v and a have the same sign.
Example: s(t) = t³ − 6t² + 9t. When is it at rest?
- v = 3t² − 12t + 9 = 3(t − 1)(t − 3).
- At rest at t = 1 s and t = 3 s.
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