5.4.4Forces
Calculating Speed — AQA GCSE Combined Science Trilogy 8464 - Physics Revision Notes & Topical Questions
5 min read 11 parts Lesson 21 of 44
Part 1 of 9The speed equation
Equation
- Equation speed = distance travelled ÷ time taken, or v = s ÷ t.
Units
- Units v in metres per second (m/s), s in metres (m), t in seconds (s).
Rearranging
- Rearranging distance s = v × t and time t = s ÷ v.
- A formula triangle with s on top and v, t below can help.
Part 2 of 9Constant and non-uniform motion
| Type of motion | What the speed does | Equation used |
|---|---|---|
| Constant (uniform) speed | Stays the same | v = s ÷ t |
| Non-uniform motion | Speeds up or slows down | average speed = total distance ÷ total time |
| Sprinter in a race | Accelerates, then holds a top speed | Average speed over the whole race |
Part 3 of 9Worked example: distance of a flight
1
A plane flies at 250 m/s for 2 hours. List v = 250 m/s and t = 2 hours.
2
Write v = s ÷ t and rearrange to s = v × t.
3
Convert the time to seconds: 2 × 60 × 60 = 7200 s.
4
Substitute: s = 250 × 7200 = 1 800 000 m.
5
State the answer with units: 1 800 000 m, which is 1800 km.
Part 4 of 9Worked example: average speed
1Record-setting sprint
- Record-setting sprint A 100 m sprint is run in 10.49 s.
2Speed changes
- Speed changes The sprinter speeds up from the blocks, so the speed is not constant.
3Use average speed
- Use average speed average speed = 100 ÷ 10.49.
4Result
- Result About 9.53 m/s.
Part 5 of 9Unit checklist
Before substituting
Distance
- Distance Convert kilometres to metres by multiplying by 1000.
Time
- Time Convert minutes to seconds by multiplying by 60 and hours by 3600.
Final answer
- Final answer Write m/s, and check the value is sensible compared with typical speeds.
Part 6 of 9Converting between units
| Conversion | Method | Example |
|---|---|---|
| km to m | Multiply by 1000 | 18 km = 18 000 m |
| minutes to seconds | Multiply by 60 | 15 min = 900 s |
| hours to seconds | Multiply by 3600 | 0.5 h = 1800 s |
| km/h to m/s | Divide by 3.6 | 72 km/h = 20 m/s |
| m/s to km/h | Multiply by 3.6 | 15 m/s = 54 km/h |
Part 7 of 9Worked example: a car journey
1
A car travels 18 km in 15 minutes. Convert to the correct units: 18 km = 18 000 m and 15 min = 900 s.
2
Write the equation: v = s ÷ t.
3
Substitute: v = 18 000 ÷ 900 = 20 m/s.
4
Check against typical values: 20 m/s is about 72 km/h, a sensible speed for a car on a main road.
Part 8 of 9Finding the time
Rearranged equation
- Rearranged equation When the question asks for time, use t = s ÷ v.
Example
- Example Sound travels at about 330 m/s.
- To cross 1320 m it takes t = 1320 ÷ 330 = 4 s, which is why you hear thunder several seconds after the lightning.
Part 9 of 9Checking an answer
Is the number sensible?
Compare with typical values
- Compare with typical values A walking speed of 40 m/s or a car speed of 0.5 m/s should make you stop and check your working.
Check the units
- Check the units If the distance is in metres and the time in seconds, the answer is in m/s.
- A mixture of units is the commonest cause of a wrong answer.
Significant figures
- Significant figures Give the answer to the same number of significant figures as the least precise data in the question,
- or to two or three if none is stated.
Key terms
| Term | Meaning |
|---|---|
| Speed | The rate of change of distance, found by dividing distance by time. |
| Average speed | The total distance travelled divided by the total time taken. |
| Uniform motion | Motion at a constant speed. |
| Non-uniform motion | Motion in which the speed changes. |
| Formula triangle | A memory aid for rearranging an equation with three quantities. |
Avoid these mistakes
1
Substituting minutes or kilometres directly when the equation needs seconds and metres.
2
Rearranging wronglydistance is speed multiplied by time, not divided.
3
Treating the average speed as the speed at every moment of the journey.
4
Rounding too early in the calculation, or leaving out the unit.
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