In the bike race scenario where Greg’s speed was measured as 13.5 mph at mile marker 4 (out of 10), which statement best describes the measured number? A) It is the instantaneous speed of the bike rider. B) It is the instantaneous velocity of the bike rider. C) It is the average velocity of the bike rider. D) It is the average speed of the bike rider.

What the measurement at “mile marker 4” is telling you

A speed given at a particular point along the course is meant to describe Greg’s motion right then, at that location. That is the idea of an instantaneous measurement.

Speed vs. velocity

• Speed is how fast something moves (a scalar), reported in mph.
• Velocity includes both speed and direction (a vector).

The statement only says “13.5 mph,” with no direction, so it matches speed, not velocity.

Why it is not an average

Average speed or average velocity require an interval, for example: $$\text{average speed} = \frac{\text{total distance}}{\text{total time}}$$

Here, we are not given a time interval or a start and end segment over which to average. The problem says the speed was measured at mile marker 4, which points to an instantaneous value.

Picking the best option

• A is correct: instantaneous speed.
• B is wrong: velocity would need direction.
• C and D are wrong: averages require an interval, not just a single point measurement.