Why do some rides feel faster than others?
Ever wondered why a bike can zip down a hill faster than on flat ground, even though you’re pedalling the same? The secret lies in the ideas of speed, velocity and acceleration – the three friends that describe motion.
💡 In Simple Words: Speed tells how fast something moves, velocity adds the direction, and acceleration tells how quickly the speed or direction changes.
What is Speed?
Definition
Speed is the distance covered per unit of time. Think of it like the number of pages you read per minute – it only cares about how many pages, not whether you’re reading forward or backward.
How to calculate speed
Use the formula Speed = Distance ÷ Time. Both distance and time must be in the same units (like metres and seconds, or kilometres and hours).
Worked example
A car travels 150 km in 3 hours. Its speed is:
Speed = 150 km ÷ 3 h = 50 km/h.
What is Velocity?
Definition
Velocity is speed with a direction attached. Imagine you’re walking 5 blocks north – the “north” part makes it a velocity, not just a speed.
How to calculate velocity
Use the same formula as speed, but always write the direction after the number (e.g., 20 m/s east).
Worked example
A runner covers 200 metres north in 25 seconds.
Velocity = 200 m ÷ 25 s = 8 m/s north.
What is Acceleration?
Definition
Acceleration measures how quickly velocity changes. It can be a change in speed, a change in direction, or both. Picture pressing the gas pedal: the faster you press, the higher the acceleration.
How to calculate acceleration
Formula: Acceleration = (Final velocity – Initial velocity) ÷ Time taken. Units are metres per second squared (m/s²).
Worked example
A scooter speeds up from 2 m/s to 12 m/s in 5 seconds.
Acceleration = (12 m/s – 2 m/s) ÷ 5 s = 2 m/s².
Speed, Velocity and Acceleration – How are they related?
All three describe motion, but each adds a layer of detail:
- Speed = "how fast" (magnitude only).
- Velocity = "how fast and which way" (magnitude + direction).
- Acceleration = "how quickly the velocity changes" (rate of change of velocity).
Quick Comparison Table
| Concept | What it tells you | Units | Direction needed? |
|---|---|---|---|
| Speed | Distance per time | m/s or km/h | No |
| Velocity | Distance per time with direction | m/s or km/h (e.g., east) | Yes |
| Acceleration | Change in velocity per time | m/s² | Depends on change (speed or direction) |
Common Mistakes to Avoid
- Mixing up speed and velocity – remember direction matters for velocity.
- Using wrong units – always keep distance and time in compatible units.
- Ignoring sign in acceleration – a negative sign means slowing down (deceleration) or a change in direction.
📝 Likely Exam Questions
- Define speed, velocity and acceleration.
Answer: Speed is distance covered per unit time (scalar). Velocity is speed with a specified direction (vector). Acceleration is the rate of change of velocity per unit time (vector). - A car moves 120 km north in 2 hours. Find its speed and velocity.
Answer: Speed = 120 km ÷ 2 h = 60 km/h. Velocity = 60 km/h north. - If a bike accelerates from 5 m/s to 15 m/s in 4 s, what is its acceleration?
Answer: Acceleration = (15 – 5) m/s ÷ 4 s = 2.5 m/s². - Explain why a runner who changes direction while keeping the same speed is still accelerating.
Answer: Acceleration depends on any change in velocity. Changing direction changes the velocity vector, so even with constant speed, the runner has acceleration. - Calculate the average speed of a train that travels 90 km at 30 km/h and then 150 km at 50 km/h.
Answer: Total distance = 240 km. Time = 90÷30 + 150÷50 = 3 h + 3 h = 6 h. Average speed = 240 km ÷ 6 h = 40 km/h.