The average velocity of an object over a given period of time is found by dividing the distance it has traveled by the time elapsed. Because velocity refers to the rate at which an object changes position, it is a vector quantity and direction matters. This differentiates average velocity from average speed. The formula for average velocity is (the change in x) / (the change in t) or (x_{2}-x_{1}) / (t_{2}-t_{1}).

Analyzing the difference between average speed and average velocity.

Instantaneous Velocity

Instantaneous velocity is the velocity of an object in motion at a specific point in time. This is determined similarly to average velocity, but we narrow the period of time so that it approaches zero. If an object has a standard velocity over a period of time, its average and instantaneous velocities may be the same. The formula for instantaneous velocity is the limit as t approaches zero of the change in d over the change in t.

Using Derivatives to Find the Instantaneous Velocity in Physics

Instantaneous Velocity, Definition of Derivative.
This video uses the definition of the derivative to find the instantaneous velocity of a particle.

Acceleration

The acceleration of an object is the change in its velocity over a period of time, or the rate at which its velocity increases. The units for acceleration are distance/time^{2} (for example m/s^{2}).

Free Fall

An object is in free fall when gravity is the only force to move it through space. In reality, free fall is affected by variables such as wind iance, but when physicists discuss free fall, they generally assume that it is taking place in a vacuum. The acceleration of an object in free fall is 9.8 m/s^{2}.

A brief introduction to free fall problems in high school and honors physics.

Graphs of Motion

The two most commonly used graphs of motion are velocity (distance v. time) and acceleration (velocity v. time). In each case, time is shown on the x-axis. The graph of velocity is a curve while the graph of acceleration is linear. The slope of a line tangent to the graph of distance v. time is its instantaneous velocity. The slope of a line tangent to velocity v. time is its acceleration.

Drawing and interpreting graphs of motion.

A brief review of particle diagrams and motion graphs

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