Average Velocity, Average Speed, and a First Look at Acceleration

If your phone's GPS tells you your average speed on a trip was 45 mph, were you actually going 45 mph the whole time? Almost certainly not — and that gap between "the summary number" and "what was actually happening the whole time" is exactly what this lesson formalizes.

Picture a road trip: you drive 120 miles over 2 hours, but you end up only 90 miles north of where you started — some of those miles were spent winding around, not making progress toward your destination. That gap between "how much ground you covered" and "how far you ended up" is exactly the difference between speed and velocity, and it shows up every time direction changes along the way.

Average speed is total distance divided by total time — it only cares about how much ground you covered, not which way you were pointed. Average velocity is total displacement divided by total time — it only cares about your straight-line change in position, start to finish. In that road trip, average speed is $\dfrac{120\text{ mi}}{2\text{ hr}} = 60$ mph, while average velocity is $\dfrac{90\text{ mi}}{2\text{ hr}} = 45$ mph. Same trip, two different — and both correct — numbers, because they're answering different questions.

The gap gets even more dramatic on a round trip. Run a lap around a track and finish exactly where you started, and your average speed is a perfectly normal positive number — but your average velocity is zero, because your displacement (start point to end point) is zero. That's not a contradiction; it's the whole point of having two separate quantities. A classmate who says "the average velocity is zero, so the object didn't move" is missing the distinction — the object moved plenty, it just didn't end up anywhere new.

That same road trip hints at a third idea: were you actually going 45 mph the entire time? No — you sped up leaving the driveway and slowed down at red lights, so your velocity itself was constantly changing. The rate at which velocity changes over time is called acceleration, written $a = \dfrac{\Delta v}{\Delta t}$. It gets a full lesson of its own soon, but it's worth introducing now: speed and velocity describe how you're moving, while acceleration describes how that movement is changing.

Videos

• Example Problem: Velocity and Speed are Different — Flipping Physics
• Average Velocity Example Problem with Three Velocities — Flipping Physics

Practice Problems

1. A car travels 150 miles in 3 hours, all in the same direction. Find its average velocity.
2. A runner completes a 400 m lap (starting and finishing at the same point) in 80 s. Find the average speed and the average velocity.
3. A train travels 60 km east in 1 hour, then 20 km west in 30 minutes. Find the average speed and average velocity for the whole trip.
4. A delivery van covers 3 legs of a trip: 10 km in 15 min, 8 km in 10 min, and 12 km in 20 min, all in the same direction. Find the average velocity for the entire trip (hint: use total distance and total time, not the average of the three individual speeds).
5. A swimmer completes 4 laps of a 50 m pool (200 m total) in 3 minutes, ending back at the starting wall. Find the average speed and average velocity for the swim.
6. A cyclist rides 12 km east in 40 minutes, then rides back west, arriving home a total of 100 minutes after starting. a) Find the average speed for the entire trip. b) Find the average velocity for the entire trip. c) A classmate says "since the average velocity is smaller than the average speed, the cyclist must have pedaled slower on the way back." Explain why this reasoning is flawed.
7. A hiker's average velocity for a 2-hour hike is 1.5 km/h north. If the hike had instead taken 3 hours to cover the exact same net displacement, would the average velocity increase, decrease, or stay the same? Explain your reasoning first, then calculate the new average velocity to check.