Average speed is defined as the total distance traveled divided by the total time taken for that journey.

Instantaneous speed, on the other hand, refers to the speed of an object at a specific moment in time. This value is typically calculated using calculus and represents the limit of the average speed as the time interval approaches zero. In essence, instantaneous speed reflects the speed at a precise moment rather than an average over an extended period.

To compute average speed, we can use the following formula:

For instance, if a car travels $100$ miles in $2$ hours, we can calculate its average speed as follows:

Conversely, instantaneous speed is determined using calculus. To find the instantaneous speed of an object at a specific time, we compute the derivative of its position function with respect to time. This derivative represents the slope of the tangent line to the position function at that particular point in time.

For example, consider an object’s position function defined as:

To find the instantaneous speed at time $t = 2$, we first calculate the derivative of the position function:

Next, we substitute $t = 2$ into the derivative to determine the instantaneous speed:

Thus, the object’s instantaneous speed at time $t = 2$ is $11$ units per time (which could be in meters per second, miles per hour, etc.).