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 is how fast something moves — distance divided by time: \[ \text{speed} = \dfrac{\text{distance}}{\text{time}}. \] A car that travels \(100\) miles in \(2\) hours has a speed of \(50\) miles per hour. Velocity is speed with a direction — for example, \(50\) mph north. On the test, if a question mentions direction, it is talking about velocity; if it only cares about how fast, it is speed.
Acceleration
Acceleration is how quickly velocity changes — speeding up, slowing down, or changing direction. It is the change in velocity divided by the time it takes: \[ \text{acceleration} = \dfrac{\text{change in velocity}}{\text{time}}. \] If a car speeds up from \(0\) to \(20\) m/s in \(4\) seconds, its acceleration is \[ \dfrac{20-0}{4} = 5 \text{ m/s}^2. \] A negative acceleration means slowing down. Notice acceleration is about changing speed, not just moving fast — a car at a steady \(60\) mph has zero acceleration.
Telling Them Apart
Here is the quick summary. Speed is distance over 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. But for most test questions, 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
- Speed = distance divided by time.
- Velocity = speed with a direction.
- Acceleration = change in velocity divided by time.
- Steady speed in a straight line means zero acceleration.
Practice
- A runner covers \(400\) m in \(50\) s. What is the speed?
- What makes velocity different from speed?
- A car goes from \(10\) m/s to \(30\) m/s in \(5\) s. What is the acceleration?
- Does a car at a constant \(40\) mph in a straight line have any acceleration?
- What does a negative acceleration mean?
- Write the formula for speed.
Answers
- \(\dfrac{400}{50} = 8 \text{ m/s}\).
- Velocity includes a direction.
- \(\dfrac{30-10}{5} = 4 \text{ m/s}^2\).
- No, its acceleration is zero.
- The object is slowing down.
- \(\text{speed} = \dfrac{\text{distance}}{\text{time}}\).
Where This Fits in Your Science Prep
Motion sets up forces and Newton’s laws, which explain what causes acceleration, and it uses the same formula skills as units and formulas. See all topics on the Science Topics Hub.
Recommended Prep Books
These study guides and practice books help you keep building momentum as you prepare:
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