✏️ Quick & colourful revision notes — by @edugrown
📚 Table of Contents
1
Motion & Position
Everything around us is moving — butterflies, cars, planets, even dust particles! To study such a huge variety of motion easily, scientists study it in simple, idealised forms: linear motion (straight line), circular motion and oscillatory motion.
🔹 What is Motion?
DEFINITION
An object is said to be in motion if its position changes with time w.r.t a fixed reference point. If position does not change, the object is at rest.
An object is said to be in motion if its position changes with time w.r.t a fixed reference point. If position does not change, the object is at rest.
🔹 Describing Position
- First fix a reference point (origin, O).
- Position = distance + direction from the reference point.
- On a straight line: right of O = positive (+), left of O = negative (–).
REMEMBER
An instant of time = one clock reading. A time interval = duration between two clock readings. They are NOT the same thing!
An instant of time = one clock reading. A time interval = duration between two clock readings. They are NOT the same thing!
2
Distance & Displacement
| Distance Travelled | Displacement |
|---|---|
| Total path length covered | Net change in position (shortest gap between start & end) |
| Only magnitude (scalar) | Magnitude + direction (vector) |
| Can never decrease | Can be zero even if object moved a lot! |
| SI unit: metre (m) | SI unit: metre (m) |
KEY RULE
Distance travelled ≥ magnitude of displacement.
They are equal only when the object moves in one direction only (no turning back).
Distance travelled ≥ magnitude of displacement.
They are equal only when the object moves in one direction only (no turning back).
3
Average Speed & Velocity
FORMULA
Average Speed = Total distance travelled ÷ Time interval
SI unit: m/s (also km/h)
FORMULA
Average Velocity = Displacement ÷ Time interval (vav = s / t)
SI unit: m/s — direction = direction of displacement
- Speed has no direction (scalar). Velocity has magnitude + direction (vector).
- Uniform motion: equal distances in equal time intervals → constant speed.
- Non-uniform motion: unequal distances in equal time intervals → speed changes.
- “Velocity” (without a time interval) usually means instantaneous velocity — velocity at one particular instant (like a speedometer reading + direction of tyres).
QUICK EXAMPLE
Sarang swims one length & comes back in 50 s in a 25 m pool.
Distance = 50 m → Speed = 50/50 = 1 m/s
Displacement = 0 m → Velocity = 0/50 = 0 m/s
Sarang swims one length & comes back in 50 s in a 25 m pool.
Distance = 50 m → Speed = 50/50 = 1 m/s
Displacement = 0 m → Velocity = 0/50 = 0 m/s
4
Average Acceleration
DEFINITION
The rate of change of velocity with time. It tells us how quickly velocity is changing (jolt when a vehicle starts/stops suddenly!).
The rate of change of velocity with time. It tells us how quickly velocity is changing (jolt when a vehicle starts/stops suddenly!).
FORMULA
a = (v − u) / t
u = initial velocity, v = final velocity, t = time taken · SI unit: m/s²
- If speed increases → acceleration is in the same direction as velocity.
- If speed decreases (retardation) → acceleration is opposite to velocity direction (negative sign).
- Acceleration can happen due to change in magnitude of velocity, direction, or both.
GOOD TO KNOW
A fast-moving object can still have zero acceleration (constant velocity). Acceleration depends on how fast velocity changes, not how fast the object moves!
A fast-moving object can still have zero acceleration (constant velocity). Acceleration depends on how fast velocity changes, not how fast the object moves!
FREE FALL
When an object falls freely, its velocity increases at a constant rate of 9.8 m/s². This is called acceleration due to gravity (g).
When an object falls freely, its velocity increases at a constant rate of 9.8 m/s². This is called acceleration due to gravity (g).
5
Position–Time Graph
Shows how the position of an object changes with time. Time is plotted on the X-axis, position on the Y-axis.
| Shape of Graph | What it Means |
|---|---|
| Straight line (sloped) | Object moving with constant velocity |
| Curved line | Velocity is changing → accelerated motion |
| Straight line parallel to time-axis | Object is at rest |
| Steeper line | Higher velocity |
TIP
Slope of position-time graph = Velocity
REMEMBER
A graph is not a route map — it only shows how position changes with time w.r.t. origin, not the actual path shape.
A graph is not a route map — it only shows how position changes with time w.r.t. origin, not the actual path shape.
6
Velocity–Time Graph
Shows how velocity changes with time.
| Shape of Graph | What it Means |
|---|---|
| Line parallel to time-axis | Constant velocity → zero acceleration |
| Straight line going up | Constant (positive) acceleration |
| Straight line going down | Constant (negative) acceleration / retardation |
TIP 1
Slope of velocity-time graph = Acceleration
TIP 2
Area between graph & time-axis = Displacement
7
Kinematic Equations
For motion in a straight line with constant acceleration, these 3 equations connect u, v, a, t and s:
EQUATION 1
v = u + at
EQUATION 2
s = ut + ½at²
EQUATION 3
v² = u² + 2as
u = initial velocity
v = final velocity
a = acceleration
t = time
s = displacement
VALID ONLY WHEN
Acceleration is constant. Signs of u, v, a, s show direction in straight-line motion.
Acceleration is constant. Signs of u, v, a, s show direction in straight-line motion.
REAL-LIFE USE
Braking distance of a vehicle depends on its speed, road condition, tyre condition & driver’s reaction time — this is exactly why we must keep a safe distance from the vehicle ahead! 🚗💨
Braking distance of a vehicle depends on its speed, road condition, tyre condition & driver’s reaction time — this is exactly why we must keep a safe distance from the vehicle ahead! 🚗💨
8
Motion in a Plane
- Motion in one dimension — along a straight line (e.g. train on a straight track).
- Motion in a plane (2D) — e.g. a kicked ball’s path, a car overtaking another, a satellite’s circular path.
- Motion in space (3D) — e.g. a bird flying, a car climbing a mountain road, an aircraft in flight.
9
Uniform Circular Motion
DEFINITION
When an object moves in a circular path with constant speed, its motion is called Uniform Circular Motion (UCM).
When an object moves in a circular path with constant speed, its motion is called Uniform Circular Motion (UCM).
FORMULA
Average speed = 2πR / T
R = radius of circle, T = time for one revolution
- In one full revolution → distance = 2πR, but displacement = 0 (back to start).
- Speed stays constant, but direction of velocity keeps changing at every point (velocity is always tangent to the circle).
- Since direction changes continuously → UCM is accelerated motion, even though speed is constant!
ACTIVITY INSIGHT
When a marble moving inside a ring is suddenly released, it flies off in a straight line — tangent to the circle at that point. This shows velocity direction at any instant is along the tangent.
When a marble moving inside a ring is suddenly released, it flies off in a straight line — tangent to the circle at that point. This shows velocity direction at any instant is along the tangent.
10
Quick Formula Sheet
| Quantity | Formula |
|---|---|
| Average Speed | Total distance ÷ Time interval |
| Average Velocity | Displacement ÷ Time interval |
| Average Acceleration | (v − u) ÷ t |
| Equation 1 | v = u + at |
| Equation 2 | s = ut + ½at² |
| Equation 3 | v² = u² + 2as |
| Speed in UCM | 2πR ÷ T |
📏 Distance – scalar
➡️ Displacement – vector
🏃 Speed – scalar
🎯 Velocity – vector
⚡ Acceleration – vector
🌍 g = 9.8 m/s²
🎉 That’s a wrap!
Chapter 4 · Describing Motion Around Us — Notes by @edugrown