Which statement best describes average velocity vs. average speed?

Which statement best describes average velocity vs. average speed?

• A. Average velocity is the velocity averaged over a time interval; instantaneous velocity is the velocity at a single moment.
• B. Average velocity is always greater than instantaneous velocity.
• C. Instantaneous velocity is the same as average velocity for any motion.
• D. Average velocity is a scalar.

Answer: (A)

Average velocity tells you how fast and in what direction the position changes on average over a time interval. It’s defined as the displacement (the straight‑line change in position from the start to the end) divided by the time, and it’s a vector, so direction matters. Instantaneous velocity is the velocity at a single moment in time—the slope of the position-versus-time graph at that moment. In contrast, average speed is the total distance traveled divided by the time, and it’s a scalar, so it has no direction. This distinction matters because, for most motions that aren’t at a steady pace in a straight line, the instantaneous velocity at a moment can point in a different direction and have a different magnitude than the average velocity computed over the interval. Only if the motion is at a constant velocity in a straight line do the average velocity and the instantaneous velocity coincide. For example, if you go 100 m forward in 10 s and then 50 m backward in 5 s, the displacement is 50 m forward in 15 s, so the average velocity is about 3.3 m/s forward. The total distance is 150 m in 15 s, so the average speed is 10 m/s. The instantaneous velocity at intermediate times would reflect the changing direction and speed along the path.

Average velocity tells you how fast and in what direction the position changes on average over a time interval. It’s defined as the displacement (the straight‑line change in position from the start to the end) divided by the time, and it’s a vector, so direction matters. Instantaneous velocity is the velocity at a single moment in time—the slope of the position-versus-time graph at that moment. In contrast, average speed is the total distance traveled divided by the time, and it’s a scalar, so it has no direction.

This distinction matters because, for most motions that aren’t at a steady pace in a straight line, the instantaneous velocity at a moment can point in a different direction and have a different magnitude than the average velocity computed over the interval. Only if the motion is at a constant velocity in a straight line do the average velocity and the instantaneous velocity coincide.

For example, if you go 100 m forward in 10 s and then 50 m backward in 5 s, the displacement is 50 m forward in 15 s, so the average velocity is about 3.3 m/s forward. The total distance is 150 m in 15 s, so the average speed is 10 m/s. The instantaneous velocity at intermediate times would reflect the changing direction and speed along the path.