Motion: Speed, Velocity, and Acceleration

Motion is one of the most testable areas of physical science, and it starts with three closely related ideas: speed, velocity, and acceleration. They sound similar but mean different things, and each has a simple formula. Learn to tell them apart and the calculations follow easily.

Speed and Velocity

Speed tells how fast something moves. Average speed is total distance divided by elapsed time: \[ \text{average speed} = \dfrac{\text{distance}}{\text{time}}. \] A car that travels \(100\) miles in \(2\) hours has an average speed of \(50\) miles per hour. Velocity includes speed and direction. For example, \(50\) mph north. A velocity answer must specify a direction; a speed answer gives only how fast the object moves.

Acceleration

Acceleration tells how quickly velocity changes. Speeding up, slowing down, and turning all count. Average acceleration is the change in velocity divided by the elapsed time: \[ \text{average acceleration} = \dfrac{\text{change in velocity}}{\text{time}}. \] If a car speeds up from \(0\) to \(20\) m/s in \(4\) seconds, its acceleration is \[ \dfrac{20-0}{4} = 5 \text{ m/s}^2. \] Negative acceleration points in the chosen negative direction. In one-dimensional motion, an object slows down when velocity and acceleration have opposite signs, and speeds up when they have the same sign. Acceleration depends on a change in velocity. A car moving at a steady \(60\) mph in a straight line has zero acceleration.

Telling Them Apart

Here is the quick summary. Average speed is total distance over elapsed time. Velocity is speed plus a direction. Acceleration is how fast velocity changes. A common trap: constant speed does not mean zero acceleration if the direction is changing. A car going around a curve at a steady speed is still accelerating because its direction changes. Moving at a steady speed in a straight line means no acceleration.

Watch: A Short Video Lesson

2 Minute Classroom walks through this skill clearly in a few minutes. It is a helpful companion to the reading above:

A Routine for Motion Questions

1. Average speed = total distance divided by elapsed time.
2. Velocity = speed with a direction.
3. Average acceleration = change in velocity divided by elapsed time.
4. Steady speed in a straight line means zero acceleration.

Practice

1. A runner covers \(400\) m in \(50\) s. What is the average speed?
2. What makes velocity different from speed?
3. A car goes from \(10\) m/s to \(30\) m/s in \(5\) s. What is the average acceleration?
4. Does a car at a constant \(40\) mph in a straight line have any acceleration?
5. What does a negative acceleration mean?
6. Write the formula for average speed.

Answers

1. \(\dfrac{400}{50} = 8 \text{ m/s}\).
2. Velocity includes a direction.
3. \(\dfrac{30-10}{5} = 4 \text{ m/s}^2\).
4. No, its acceleration is zero.
5. Acceleration points in the chosen negative direction. This slows an object moving in the positive direction but speeds up one moving in the negative direction.
6. \(\text{average speed} = \dfrac{\text{distance}}{\text{time}}\).

Keep studying

High School Physics includes 12 full-length practice tests: two in the book and ten online.

Motion sets up forces and Newton’s laws, which explain what causes acceleration. Continue with the acceleration and free-fall lesson, or return to the High School Physics learning hub.