ICSE Class 9 Physics: Speed, Velocity and Acceleration Explained

Why does a car sometimes feel faster than a bike even when the numbers look alike?

That little puzzle is what speed, velocity and acceleration help us solve. Let’s break it down so the next time you’re on the road, you’ll see the physics behind the motion.

💡 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 speed as how fast you run, velocity as the way you run north or south, and acceleration as how quickly you speed up or slow down.

What is Speed?

Speed is the distance covered per unit of time. It’s a scalar quantity, which means it only has magnitude (a number) and no direction. Imagine water flowing through a pipe: the amount of water passing a point each second is like speed – you care only about how much, not where it’s going.

• Formula: speed = distance ÷ time
• Unit in the ICSE syllabus: metres per second (m/s) or kilometres per hour (km/h)

What is Velocity?

Velocity adds a direction to speed, making it a vector quantity (it has both magnitude and direction). If you throw a ball straight up, its velocity points upward; if you roll a ball east, its velocity points east.

• Formula: velocity = displacement ÷ time – displacement is the straight‑line change in position, not the total path length.
• Unit: same as speed (m/s or km/h), but you always write the direction, e.g., 5 m/s east.

What is Acceleration?

Acceleration tells how fast the velocity changes. It can mean the object is speeding up, slowing down, or turning. Think of a car hitting the gas pedal – the speedometer needle climbs because of acceleration.

• Formula: acceleration = change in velocity ÷ time
• Unit: metres per second squared (m/s²)
• If the velocity goes from 0 to 10 m/s in 2 seconds, acceleration = (10‑0)/2 = 5 m/s².

How Are Speed, Velocity and Acceleration Related?

All three describe motion, but they answer different questions:

• Speed → "How fast?"
• Velocity → "How fast and in which direction?"
• Acceleration → "How quickly is the speed or direction changing?"

When acceleration is zero, velocity stays constant, and speed stays constant too. When acceleration is non‑zero, either the speed changes, the direction changes, or both.

Worked Example: From Rest to a Sprint

A student runs from a stand‑still and covers 20 m in 4 seconds. Find the average speed, average velocity (assume straight line), and average acceleration if the speed increases uniformly.

1. Average speed: distance ÷ time = 20 m ÷ 4 s = 5 m/s.
2. Average velocity: displacement is also 20 m (straight line) ÷ 4 s = 5 m/s east (or whichever direction the run is).
3. Average acceleration: final speed (v) = ? Since motion is uniform acceleration, use v = u + at, where u = 0, a = ?, t = 4 s, and average speed = (u+v)/2 = 5 m/s. Solve: (0+v)/2 = 5 → v = 10 m/s. Now a = (v‑u)/t = (10‑0)/4 = 2.5 m/s².

So the runner’s speed grew from 0 to 10 m/s, averaging 5 m/s, with an acceleration of 2.5 m/s².

Quick Comparison

📝 Likely Exam Questions

1. Define speed, velocity and acceleration.
   Answer: Speed is distance per time (scalar). Velocity is displacement per time with a direction (vector). Acceleration is the rate of change of velocity per time (vector).
2. A car travels 150 km north in 3 h. Find its speed and velocity.
   Answer: Speed = 150 km ÷ 3 h = 50 km/h. Velocity = 50 km/h north.
3. If a bike increases its velocity from 2 m/s east to 8 m/s east in 3 s, what is its acceleration?
   Answer: Δv = 8‑2 = 6 m/s east. Acceleration = 6 m/s ÷ 3 s = 2 m/s² east.
4. Explain why a car moving at constant speed around a circular track is still accelerating.
   Answer: Even though speed is constant, the direction of motion constantly changes, so velocity changes. The change in direction means there is a centripetal (center‑seeking) acceleration.
5. Calculate the average acceleration of a ball that rolls from rest to 12 m/s in 4 s.
   Answer: a = (12‑0)/4 = 3 m/s².