Section 1 of 9Speed and velocity
| Feature | Speed | Velocity |
|---|---|---|
| Includes direction? | No | Yes |
| Type of quantity | Scalar | Vector |
| Example | 15 m/s | 15 m/s south |
| Unit | m/s | m/s, plus a direction |
| Can be negative? | No | Yes, when the sign shows direction |
Section 2 of 9Giving a direction
In words
- In words Directions can be given as north, south, left, right, forwards, backwards, up or down.
As a bearing
- As a bearing A velocity can be described using a compass bearing such as 030 degrees.
Using signs in calculations
- Using signs in calculations Choose one direction as positive; the opposite direction is then negative.
- It does not matter which direction is chosen positive, as long as it is used consistently.
Section 3 of 9Same speed, different velocity
Two cars at 20 m/s
Travelling the same way
- Travelling the same way Both have speed 20 m/s and velocity 20 m/s north, so their velocities are equal.
Travelling opposite ways
- Travelling opposite ways Their speeds are both 20 m/s but their velocities are 20 m/s north and 20 m/s south, which are different.
Changing direction
- Changing direction A car going round a bend at a constant speed has a changing velocity, because its direction is changing.
Section 4 of 9Stating velocity in an answer
1
Calculate the size of the velocity, using distance travelled in a given direction divided by time.
2
Decide the direction of motion from the question or diagram.
3
Write the direction in words or with a plus or minus sign.
4
Combine them: for example +12 m/s, or 12 m/s to the east.
5
Check that opposite directions have opposite signs.
Section 5 of 9Worked example: a runner out and back
1
A runner jogs 100 m east in 25 s. Taking east as positive, the velocity is +100 ÷ 25 = +4 m/s.
2
The runner then jogs 100 m back west in 20 s. West is negative, so the velocity is −100 ÷ 20 = −5 m/s.
3
The speeds are 4 m/s and 5 m/s, which are both positive, but the velocities have opposite signs because the directions are opposite.
4
Over the whole 200 m trip the displacement is zero, so the average velocity is zero even though the average speed is 200 ÷ 45 = about 4.4 m/s.
Section 6 of 9Changing velocity means acceleration
Change of speed
- Change of speed If the speed rises or falls in a straight line, the velocity changes, so the object is accelerating or decelerating.
Change of direction
- Change of direction A vector changes if either its size or its direction changes.
- A car taking a bend at a steady 15 m/s has a changing velocity and is therefore accelerating.
Circular motion
- Circular motion An object moving in a circle at constant speed always has a velocity that points in a new direction,
- so its velocity is never constant.
Section 7 of 9Quick comparison of motion quantities
| Quantity | Scalar or vector? | Unit |
|---|---|---|
| Distance | Scalar | m |
| Displacement | Vector | m, with direction |
| Speed | Scalar | m/s |
| Velocity | Vector | m/s, with direction |
| Acceleration | Vector | m/s2, with direction |
Section 8 of 9Key terms
| Term | Meaning |
|---|---|
| Velocity | Speed in a given direction; a vector quantity. |
| Speed | How fast an object moves, without regard to its direction. |
| Vector | A quantity having both magnitude and direction. |
| Scalar | A quantity having magnitude only. |
| Bearing | A direction given as an angle measured clockwise from north. |
| Resultant velocity | The velocity found by combining two velocities, taking directions into account. |
| Average velocity | Total displacement divided by total time, which is zero for any journey that ends at its starting point. |
Section 9 of 9Exam technique
1
Writing a velocity without a direction.
2
Saying that two objects with the same speed always have the same velocity.
3
Believing velocity is unchanged when direction changes but speed stays the same.
4
Switching which direction is positive part-way through a problem.
5
Ignoring signs when combining velocitiestwo velocities in opposite directions have opposite signs, so they partly cancel rather than add.
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).