Section 1 of 7Scalars and vectors in motion
Speed
- Speed Speed tells you how fast an object moves. It is a scalar quantity, so it has size (magnitude) only.
Velocity
- Velocity Velocity is speed in a stated direction, so it is a vector quantity.
- Examples are 15 m/s south, or 250 mph on a bearing of 030°.
Same speed, different velocity
- Same speed, different velocity Two cars driving at 20 m/s in opposite directions have the same speed but different velocities,
- because their directions differ.
Section 2 of 7Acceleration
Definition
- Definition Acceleration is the rate of change of velocity: how much the velocity changes every second.
Speeding up
- Speeding up When an object speeds up, its acceleration is positive.
Slowing down
- Slowing down When an object slows down, its acceleration is negative, often called deceleration.
Section 3 of 7Equations
| Quantity | Equation | Units |
|---|---|---|
| Speed (constant) | speed = distance ÷ time | m/s |
| Change in velocity | Δv = v − u | m/s |
| Acceleration | a = Δv ÷ Δt | m/s2 |
Section 4 of 7Typical speeds and why they vary
Everyday speeds
Walking and running
- Walking and running A hiker walks at about 2 m/s, a fit person can run at around 5 m/s, and a cyclist often reaches 6 to 8 m/s.
Animals
- Animals A bumble bee can fly at up to about 4.5 m/s, much slower than a cheetah, which can exceed 25 m/s in short bursts.
Vehicles
- Vehicles A car on a motorway travels at about 30 m/s, and a passenger aircraft cruises at roughly 250 m/s.
Average speed
- Average speed Real journeys involve speeding up and slowing down,
- so the equation speed = distance ÷ time gives an average speed for the whole trip rather than the speed at any one moment.
Section 5 of 7Worked examples
1
Speed: a cyclist travels 300 m in 25 s. Speed = 300 ÷ 25 = 12 m/s.
2
Acceleration: a car speeds up from 4 m/s to 16 m/s in 3 s. First find the change in velocity: Δv = 16 − 4 = 12 m/s.
3
Then divide by the time: a = 12 ÷ 3 = 4 m/s2.
4
Deceleration: a train slows from 30 m/s to 10 m/s in 8 s. Δv = 10 − 30 = −20 m/s, so a = −20 ÷ 8 = −2.5 m/s2. The negative sign shows it is slowing down.
5
Rearranging: if the acceleration and time are known, Δv = a × Δt, and the final velocity is v = u + a × Δt.
Section 6 of 7Key terms
| Term | Meaning |
|---|---|
| Scalar | A quantity with magnitude only, such as speed or distance. |
| Vector | A quantity with both magnitude and direction, such as velocity or force. |
| Velocity | Speed in a given direction. |
| Acceleration | The rate of change of velocity, measured in m/s2. |
| Deceleration | Negative acceleration, when an object slows down. |
Section 7 of 7Exam technique
1
Using the words speed and velocity as if they always mean the same thing: velocity must include a direction.
2
Writing the unit of acceleration as m/s: it is m/s2.
3
Using the final velocity instead of the change in velocity in the acceleration equation.
4
Leaving out the negative sign for deceleration.
5
Forgetting to convert minutes or kilometres into seconds and metres before calculating.
Marked practiceQuizzes for this lesson
Physics 0625 & 9702 SUVAT Mastery
Graph Interpretation
Constant Acceleration Equations (SUVAT) & Slopes
v = u + at | s = ut + ½at2 | v2 = u2 + 2as | s = ½(u + v)t
- Displacement-Time Graph: Gradient = Velocity (curve = accelerating).
- Velocity-Time Graph: Gradient = Acceleration; Area under curve = Distance travelled / Displacement.
- Free Fall in vacuum:
a = g ≈ 9.81 m/s2downwards (air resistance negligible).