Calculus II

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Velocity

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Calculus II

Definition

Velocity is a vector quantity that measures the rate of change of an object's position with respect to time. It has both magnitude and direction.

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5 Must Know Facts For Your Next Test

  1. Velocity can be found using the first derivative of the position function with respect to time: $v(t) = \frac{dx}{dt}$.
  2. The integral of velocity with respect to time gives the displacement: $\int v(t) \, dt = s(t) + C$.
  3. If acceleration is constant, velocity can be expressed as $v(t) = v_0 + at$ where $v_0$ is the initial velocity and $a$ is acceleration.
  4. In integration problems, knowing initial conditions like initial velocity ($v_0$) can help solve for constants of integration.
  5. When calculating net change in position, consider the definite integral of velocity over a specific interval: $\Delta s = \int_{a}^{b} v(t) \, dt$.

Review Questions

  • How do you calculate velocity from a given position function?
  • What does the integral of velocity represent?
  • How can you express velocity if acceleration is constant?

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