Part 1 of 5The Speed Relationship
Most motion questions at National 5 use one simple relationship, but it must be used with consistent units.
Equation
- Average speed is found from d = v t, where d is distance in metres, v is average speed in m/s and t is time in seconds.
Rearranging
- Rearranging gives v = d ÷ t for speed and t = d ÷ v for the time taken, so any one quantity can be found from the other two.
Displacement form
- With vectors the same equation applies as s = v t, where s is displacement and v is the average velocity, with direction.
Units
- Keep SI units
- metres, seconds and m/s;
- convert kilometres by multiplying by 1000 and hours by multiplying by 3600.
- metres, seconds and m/s;
Part 2 of 5Average and Instantaneous Speed
Average and Instantaneous Speed
Average speed
- This is the total distance divided by the total time, so it smooths out any speeding up and slowing down on the journey.
Instantaneous speed
- This is the speed at one particular moment, like the reading on a car speedometer at that second.
Constant speed
- If the speed never changes, the average speed and the instantaneous speed are the same at every moment.
Journey with stops
- Time spent stationary must be included in the total time when calculating the average speed of the whole journey.
| Quantity | Symbol | Unit | Type |
|---|---|---|---|
| distance | d | m | scalar |
| displacement | s | m | vector |
| speed | v | m/s | scalar |
| time | t | s | scalar |
Part 3 of 5Solving Problems
1
Write down the quantities you know and the one you need, with their units.
2
Convert every quantity into metres, seconds or m/s before calculating.
3
Choose the correct arrangement of d = v t and substitute the values.
4
Calculate, then give the answer with a sensible number of significant figures and the correct unit.
5
Check the answer is realistic, for example a walking speed near 1.5 m/s or a car near 25 m/s.
Part 4 of 5Worked Example
Question
- A train travels 180 km in 2.0 hours.
- Calculate its average speed in m/s.
- How far does a car travelling at a steady 15 m/s go in 40 s?
- Convert180 km = 180 000 m and 2.0 h = 7200 s.
- v = d ÷ t = 180 000 ÷ 7200 = 25 m/s.What the symbols mean: v = speed (m s−1) · d or s = distance (m) · t = time (s)
- For the card = v t = 15 × 40 = 600 m.
Answer Train 25 m/s; car 600 m.
Part 5 of 5Exam Checklist & Tips
1.1.4 – Key Points for the Exam
- Average speed Total distance divided by total time taken.
- Instantaneous speed The speed of an object at one particular instant.
- Average velocity Displacement divided by time, including direction.
- m/s The SI unit of speed, metres per second.
Common Mistakes
- Using kilometres and hours in a formula that needs metres and seconds.
- Leaving out stationary time when working out the average speed of a whole journey.
- Writing the unit as m or s instead of m/s for speed.
- Assuming the speedometer reading gives average speed rather than instantaneous speed.
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).