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PRACTICE / Derivatives as physical rates

Zero velocity with a nonzero slope of velocity

A cart has position x(t) = t³ − 6t² + 9t in metres, with t in seconds.

Find its acceleration at t = 1 s.

Organize the givens & assumptions
  • x(t) = t³ − 6t² + 9t
  • Time of interest: 1 s
  • Use SI units

Smooth one-dimensional motion over the interval of interest. The polynomial coefficients carry the SI units required by the position function.

  1. A+6 m/s2+6\ \mathrm{m/s^2}
  2. B4 m/s24\ \mathrm{m/s^2}
  3. C−6 m/s2-6\ \mathrm{m/s^2}
  4. D00

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