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PRACTICE / Integrals and accumulated change

A growing acceleration

A particle begins at velocity −2 m/s. Its acceleration is a(t) = 3t m/s² for 0 ≤ t ≤ 2 s, where t is measured in seconds.

Find its velocity at t = 2 s.

Organize the givens & assumptions
  • Initial velocity: −2 m/s
  • Acceleration: a(t) = 3t in SI units
  • Interval: 0 to 2 s

One-dimensional signed quantities; the coefficient 3 has units m/s³. No constant-acceleration approximation is made.

  1. A+6 m/s+6\ \mathrm{m/s}
  2. B−4 m/s-4\ \mathrm{m/s}
  3. C+4 m/s+4\ \mathrm{m/s}
  4. D+10 m/s+10\ \mathrm{m/s}

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