Velocity

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.

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?

Related terms

Acceleration: The rate of change of velocity with respect to time, often denoted as $a(t)$ or $\frac{dv}{dt}$.

Displacement: The overall change in position of an object, which can be found by integrating the velocity function.

Position Function: $s(t)$ represents an object's location at a given time; its derivative gives the object's velocity.