Ever wondered why a bike can zip past you and then slow down, even though you can’t see any invisible hand pushing it?
💡 In Simple Words: Speed tells how fast something moves, velocity adds the direction, and acceleration tells how quickly the speed or direction changes. Think of a car on a road: speed is the odometer reading, velocity points the car’s nose, and acceleration is the foot on the gas or brake.
What is Speed?
Speed is a scalar quantity – that means it only has magnitude (how much) and no direction. You calculate it by dividing the distance travelled by the time taken.
Formula: speed = distance ÷ time
Imagine water flowing through a garden hose. If 10 liters pass through in 5 seconds, the flow rate (speed) is 2 liters per second. The water’s speed doesn’t care which way the hose points.
What is Velocity?
Velocity is a vector quantity – it has both magnitude and direction. In everyday talk we often say “speed” when we really mean “velocity”, but physics keeps them separate.
Formula: velocity = displacement ÷ time
Displacement is the straight‑line distance from start to finish, not the total path length. Think of a runner who circles a track: they may run 400 m, but their displacement after one lap is zero, so their average velocity is zero.
What is Acceleration?
Acceleration tells how quickly velocity changes. It’s also a vector because a change in direction counts as acceleration.
Formula: acceleration = change in velocity ÷ time (Δv/Δt)
Picture the same garden hose, but now you turn the tap faster. The water’s speed increases – that increase per second is acceleration.
How Speed, Velocity and Acceleration Relate
All three are linked by simple equations that pop up a lot in ICSE exams.
- Speed = distance / time
- Velocity = displacement / time
- Acceleration = (final velocity – initial velocity) / time
When motion is uniform (constant acceleration), you can use the handy set of equations:
- v = u + a·t
- s = u·t + ½ a·t²
- v² = u² + 2 a·s
Here, u is the initial velocity, v the final velocity, a the acceleration, t the time, and s the distance covered.
Worked Example
A car starts from rest and reaches 20 m/s in 5 seconds. Find the acceleration and the distance travelled during this time.
Given: u = 0 m/s, v = 20 m/s, t = 5 s.
Acceleration: a = (v – u)/t = (20 – 0)/5 = 4 m/s².
Distance: Use s = u·t + ½ a·t² = 0·5 + ½·4·(5)² = 0 + 2·25 = 50 m.
So the car accelerates at 4 m/s² and covers 50 m in those 5 seconds.
Quick Comparison Table
| Property | Speed | Velocity | Acceleration |
|---|---|---|---|
| Type | Scalar (only magnitude) | Vector (magnitude + direction) | Vector (change of velocity) |
| Formula | distance/time | displacement/time | Δv/Δt |
| Units | m s⁻¹ | m s⁻¹ (with direction) | m s⁻² |
| Example | Running 10 km in 1 h → 10 km/h | Running north 10 km in 1 h → 10 km/h north | Car speeds up from 0 to 20 m/s in 5 s → 4 m/s² |
📝 Likely Exam Questions
- Define speed, velocity and acceleration. State whether each is a scalar or vector.
Answer: Speed = distance/time, scalar. Velocity = displacement/time, vector. Acceleration = change in velocity/time, vector. - A cyclist travels 120 m north in 15 s. What is his speed and velocity?
Answer: Speed = 120/15 = 8 m/s. Velocity = 8 m/s north. - If a ball’s velocity changes from 5 m/s east to 5 m/s west in 2 s, find its acceleration.
Answer: Δv = 5 m/s west – 5 m/s east = –10 m/s (west). a = –10/2 = –5 m/s² (west). - Using the equation v = u + at, calculate the final speed of a train that starts at 30 m/s and accelerates at 0.5 m/s² for 40 s.
Answer: v = 30 + 0.5·40 = 30 + 20 = 50 m/s. - Explain why a car moving at constant speed around a circular track is accelerating.
Answer: Even though the speed is constant, the direction continuously changes, so the velocity changes. Changing direction means acceleration (centripetal acceleration).