Describing motion
To describe how something moves, we need to know how far it goes, how long it takes, and in what direction.
Speed
Speed is distance divided by time:
speed = distance ÷ time (v = d ÷ t)
Units: metres per second (m/s) or kilometres per hour (km/h).
Example: A runner covers 100 m in 12.5 s. Speed = 100 ÷ 12.5 = 8 m/s.
Average speed is total distance divided by total time. Instantaneous speed is the speed at one moment, like a car’s speedometer.
To convert: 1 m/s = 3.6 km/h. So 8 m/s = 28.8 km/h.
Velocity
Velocity is speed in a given direction: 20 m/s north. Two cars can have the same speed but different velocities if they’re going opposite ways. A car driving around a curve at constant speed has a changing velocity because its direction changes.
Acceleration
Acceleration is how quickly velocity changes:
acceleration = (final velocity − initial velocity) ÷ time
a = (v_f − v_i) ÷ t
Units: m/s² (metres per second per second).
| Situation | Type of acceleration |
|---|---|
| Car speeding up from a stoplight | Positive (speeding up) |
| Bike braking | Negative (slowing down, also called deceleration) |
| Car going around a curve at steady speed | Changing direction |
Example: A car goes from 0 to 27 m/s (about 100 km/h) in 9 s. a = (27 − 0) ÷ 9 = 3 m/s².
Distance–time graphs
| Graph shape | Meaning |
|---|---|
| Horizontal line | Stopped |
| Straight sloped line | Constant speed |
| Steeper line | Faster |
| Curve getting steeper | Speeding up |
The slope of a distance–time graph equals speed.
Forces and acceleration
When forces act on an object, we add them to find the net force.
- Forces in the same direction add: 10 N + 5 N = 15 N.
- Forces in opposite directions subtract: 10 N right − 4 N left = 6 N right.
If the net force is zero, the forces are balanced and motion doesn’t change. If the net force isn’t zero, the object accelerates in the direction of the net force.
Free-body diagrams
A free-body diagram shows an object as a box with arrows for each force. Longer arrows mean larger forces.
A sled being pulled across snow has:
- the pull (forward)
- friction (backward)
- gravity (down)
- the normal force from the ground (up)
Newton’s second law
force = mass × acceleration (F = ma)
- More force → more acceleration.
- More mass → less acceleration for the same force.
Example: What force accelerates a 1200 kg car at 2 m/s²? F = 1200 × 2 = 2400 N.
Inertia
Inertia is the tendency of an object to resist changes in its motion. Objects with more mass have more inertia.
- When a bus stops suddenly, you lurch forward because your body keeps moving.
- It’s harder to push a stalled truck than a shopping cart.
- Seat belts and airbags protect you from your own inertia in a crash.
Common mistakes
- Mixing up speed and velocity. Velocity includes direction.
- Thinking acceleration only means speeding up. Slowing down and turning are also acceleration.
- Forgetting units, especially the "squared" in m/s².
Try it yourself
- A cyclist rides 15 km in 45 minutes. What is her average speed in km/h?
- A ball rolling at 6 m/s stops in 3 s. What is its acceleration?
- Two people push a box: 40 N right and 25 N left. What is the net force?
- What acceleration does a 50 N force give a 10 kg wagon?
(Answers: 20 km/h; −2 m/s²; 15 N right; 5 m/s²)
Quick recap
- Speed = distance ÷ time; velocity is speed with direction.
- Acceleration is the rate of change of velocity.
- Net force is the combined effect of all forces.
- F = ma links force, mass and acceleration.
- Inertia is resistance to changes in motion; more mass means more inertia.