Speed

Definition

Speed is the magnitude of velocity and indicates how fast an object is moving, without regard to direction. It is a scalar quantity typically measured in units such as meters per second (m/s).

5 Must Know Facts For Your Next Test

1. Speed is calculated as the absolute value of the derivative of position with respect to time: $|v(t)| = |\frac{dx}{dt}|$.
2. Unlike velocity, speed does not have a directional component; it only measures how fast an object moves.
3. In calculus, instantaneous speed at a specific time can be found by evaluating the magnitude of the derivative at that time.
4. The average speed over an interval is given by the total distance traveled divided by the total time taken: $\text{Average Speed} = \frac{\text{Total Distance}}{\text{Total Time}}$.
5. Speed can never be negative because it represents a magnitude.

Review Questions

• How do you calculate instantaneous speed using derivatives?
• What is the difference between speed and velocity?
• How do you determine average speed over a given time interval?

Related terms

Velocity: A vector quantity that describes both the speed and direction of an object's motion.

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

Derivative: A mathematical concept that represents the rate at which a function is changing at any given point.