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PRACTICE / Derivatives as physical rates

Acceleration from a speed-position law

A particle moves in the positive x direction with v(x) = √(4 + 6x) m/s when x is measured in metres.

Find its acceleration where this motion law applies.

Organize the givens & assumptions
  • v² = 4 + 6x in SI units
  • Motion is in the positive x direction
  • Domain: x > −2/3 m

The speed is positive and differentiable on x > −2/3 m. Interpret the constants with the units required by v² = 4 + 6x.

  1. A6 m/s26\ \mathrm{m/s^2}
  2. B00
  3. C1.5 m/s21.5\ \mathrm{m/s^2}
  4. D3 m/s23\ \mathrm{m/s^2}

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