- Use speed, average speed and acceleration equations with correct units.
- Distinguish instantaneous and average motion quantities.
- Use signs consistently for direction and deceleration.
- Describe uniform and non-uniform acceleration.
3.1 Speed and velocity
Speed is distance travelled per unit time. In symbols, v = s/t. The SI unit is m s⁻¹. Velocity is the rate of change of displacement and includes direction. In one-dimensional problems, a sign convention is used: one direction is positive and the opposite is negative.
Average speed is total distance divided by total time, including time spent stationary. It is not usually equal to the simple average of two speeds unless equal times are spent at each speed. When equal distances are travelled at different speeds, the slower part occupies more time and therefore has a stronger effect on the average.
3.2 Acceleration
Acceleration is change in velocity per unit time: a = Δv/Δt = (v − u)/t. The unit is m s⁻². Acceleration occurs when speed changes, direction changes, or both. Therefore, an object moving around a circle at constant speed is accelerating because its velocity direction continuously changes.
Uniform acceleration means velocity changes by equal amounts in equal time intervals. Non-uniform acceleration means the rate of change is not constant. Deceleration is acceleration opposite to the chosen positive direction; it is represented by a negative value in a consistent sign convention.
3.3 Free fall near Earth
Near Earth’s surface and with air resistance neglected, freely falling objects have approximately constant downward acceleration g = 9.8 m s⁻². Their mass does not change the gravitational acceleration. A heavier object has a greater weight but also greater inertia, so these effects balance in ideal free fall.
In real air, drag becomes important. Shape and cross-sectional area can cause objects of equal mass to fall differently. A crumpled paper falls faster than a flat sheet because it experiences less drag relative to its weight.
3.4 Unit conversion
To convert km h⁻¹ to m s⁻¹, divide by 3.6. To convert m s⁻¹ to km h⁻¹, multiply by 3.6. Always convert all quantities to compatible units before substituting into an equation.
Use a calculator display sensibly. A final answer should normally have the same number of significant figures as the least precise data, unless the question indicates otherwise. Keep extra digits during intermediate steps and round only at the end.
Worked examples
A bus travels 600 m in 50 s, waits 20 s, then travels 900 m in 60 s. Total distance = 1500 m and total time = 130 s. Average speed = 11.5 m s⁻¹.
A cyclist’s velocity changes from 4.0 m s⁻¹ east to 10.0 m s⁻¹ east in 3.0 s. a = (10.0−4.0)/3.0 = 2.0 m s⁻² east.
Take east as positive. A ball changes from +6 m s⁻¹ to −2 m s⁻¹ in 0.50 s. a = (−2−6)/0.50 = −16 m s⁻², meaning 16 m s⁻² west.
Practical focus
Use a ticker timer, motion sensor or video frames to obtain positions at equal time intervals. Increasing spacing indicates acceleration; equal spacing indicates constant speed. Plot the data rather than relying only on visual judgement.
Examination guidance
- Write the defining equation before substituting values.
- Include stationary time in average-speed calculations.
- A negative velocity is not necessarily slowing down; it may simply mean motion in the negative direction.
Check your understanding
- Convert 72 km h⁻¹ to m s⁻¹.
- A car slows from 18 m s⁻¹ to 6 m s⁻¹ in 4 s. Find acceleration.
- What is the acceleration of an object moving at constant velocity?
- 72/3.6 = 20 m s⁻¹.
- (6−18)/4 = −3.0 m s⁻².
- Zero.
