Speed is how fast an object moves. Velocity is speed in a stated direction. If the direction changes, the velocity changes, so the object accelerates even when the speed does not.
This lesson is part of selecting and checking a physical model in SPM Physics. It extends interpreting displacement, velocity and acceleration.
How do I show the velocity change?
Take a car on a circular track at a constant speed of 10 m s⁻¹. At point A the velocity is 10 m s⁻¹ east. A quarter of a lap later, at point B, the velocity is 10 m s⁻¹ north.
The speed is the same at both points. The velocity is not, because one arrow points east and the other north. Subtract the two vectors: the change in velocity is the vector from the east arrow to the north arrow.
The change has magnitude √(10² + 10²) = √200 ≈ 14.1 m s⁻¹, directed towards the north-west, which is towards the centre of the track.
Worked example: a quarter of a lap
The quarter-turn is a 100 m arc, so it takes 10 s at this speed. Find the magnitude of the average acceleration.
Average acceleration = change in velocity ÷ time = 14.1 ÷ 10 ≈ 1.4 m s⁻². It points towards the north-west, which is towards the centre of the circle.
An exam answer needs only three ideas: the speed is constant, the direction changes, so the velocity changes and there is an acceleration. The number is a bonus when the question asks for it.
What happens over a whole lap?
The same track is 400 m round, and one lap takes 40 s at the same constant speed.
Average speed = distance ÷ time = 400 ÷ 40 = 10 m s⁻¹. Average velocity = displacement ÷ time = 0 ÷ 40 = 0 m s⁻¹, because the car returns to its start.
Average speed and average velocity answer different questions. One describes how much ground was covered, and the other describes how far the car ended up from where it began.
The mistake to avoid
The common mistake is to write “no acceleration because the speed is constant”. The wording below fixes it.
| Wrong | Right |
|---|---|
| Speed is constant, so acceleration is zero. | Speed is constant but direction changes, so velocity changes and there is an acceleration. |
| Average velocity = 10 m s⁻¹ for the lap. | Average velocity = 0 because displacement is zero. |
The same idea applies to a ball thrown upward. At the top, the velocity is zero for an instant, but the acceleration is still 10 m s⁻² downward, because the velocity is still changing.
Check yourself
A satellite moves around a circular orbit at a constant speed. A student says, “there is no resultant force because the speed does not change.” Correct the statement.
Answer
The speed is constant, but the direction of the velocity changes continuously, so the velocity changes and there is an acceleration. By Newton’s second law, an acceleration needs a resultant force. The resultant force points towards the centre of the orbit.
What to study next
Continue with using dimensions to detect an incorrect formula substitution. You can also watch the change in velocity in the motion graph explorer, and test the idea in the integrated practice set.
If you want a teacher to question your wording with you, see online one-to-one Physics tuition.