Instantaneous Velocity and Speed

To find the velocity at a specific time, called the instantaneous velocity, we take the limit of the average velocity as the time interval becomes very small. Mathematically, this process defines the derivative of the position with respect to time,

The instantaneous velocity can be found as the slope of the tangent to the curve on an x versus t graph at that particular time.

The average velocity from t=5 s to 7s is marked in the graph. Use the slider 1 (Dt) below the graph to reduce the time interval (Dt) to near zero and watch how the velocity changes.

Average Velocity from  tinitial:    to    tfinal:    is    equal to  

slider 1

slider 2

Compare this with the exact value of the  instantaneous velocity found by taking the derivative. You can also use the slider 2 to get the instantaneous velocity at some other point.

Instantaneous velocity at t= is

The speed is the magnitude of the velocity.