Science · Class 9 · Chapter 4

Describing Motion Around Us

• Distance / Displacement — Total path length / net change in position.
• Scalar / Vector — Magnitude only / magnitude and direction.
• Average speed / velocity — Distance / time / displacement / time.
• Uniform / Non-uniform motion — Constant speed / changing speed.
• Average acceleration — Change in velocity ÷ time interval.
• Slope — Velocity on a position-time graph; acceleration on a velocity-time graph.
• Kinematic equations — v=u+at, s=ut+½at², v²=u²+2as.
• Uniform circular motion — Circular motion at constant speed.

Chapter 4 · Concept 1 of 11

Position, Distance, and Displacement

• Distance travelled — The entire path length covered — a scalar, magnitude only.
• Displacement — The net change in position between two instants — a vector, with both magnitude and direction.

Chapter 4 · Concept 2 of 11

A Ball Thrown Up and Caught Again

• Distance and displacement are equal only when an object never turns back.
• Thrown up, caught at the same spot — Total distance travelled = up + down (added together). Displacement = 0, since the ball ends up exactly where it started.

Chapter 4 · Concept 3 of 11

Average Speed and Average Velocity

• Average speed — Total distance ÷ time interval. A scalar — no direction.
• Average velocity — Displacement ÷ time interval. A vector — direction matches the displacement. SI unit for both: m/s.

Chapter 4 · Concept 4 of 11

Uniform and Non-uniform Motion

• Uniform motion — Equal distances covered in equal time intervals — constant speed.
• Non-uniform motion — Unequal distances covered in equal time intervals — changing speed.

Chapter 4 · Concept 5 of 11

Average Acceleration

• Average acceleration = change in velocity ÷ time interval. SI unit: m/s².
• Speed and acceleration aren't the same — An object moving very fast at a constant velocity has zero acceleration — acceleration depends on how quickly velocity changes, not on speed itself.

Chapter 4 · Concept 6 of 11

Position-Time Graphs

• Constant velocity (straight line)
• Changing velocity (curved line)

Chapter 4 · Concept 7 of 11

Velocity-Time Graphs

• Constant positive acceleration
• Constant negative acceleration (braking)

Chapter 4 · Concept 8 of 11

Slope and Area Under the Graph

• The slope — On a position-time graph, slope = velocity. On a velocity-time graph, slope = acceleration.
• The area — The area enclosed between a velocity-time graph's line and the time axis equals the displacement.

Chapter 4 · Concept 9 of 11

The Three Kinematic Equations

• u = initial velocity, v = final velocity, a = constant acceleration, t = time, s = displacement.
• Equation | Relates
• v = u + at — Final velocity to time
• s = ut + ½at² — Displacement to time
• v² = u² + 2as — Final velocity to displacement

Chapter 4 · Concept 10 of 11

Motion in a Plane and Circular Motion

• Two dimensions — Motion confined to a flat plane — like a kicked ball's path, or a vehicle overtaking another.
• Circular motion — Movement along a circular path. Distance in one revolution = 2πR (circumference); displacement after one full revolution = 0.

Chapter 4 · Concept 11 of 11

Uniform Circular Motion Is Still Accelerated

• Uniform circular motion means constant speed along a circular path.
• Direction keeps changing — Even though speed never changes, the direction of velocity constantly does — so the motion is still accelerated, just from a change in direction, not speed.

Quick Recap

Check Your Understanding

1. 1My father walked 250 m from home to a shop, came back for a forgotten bag, went to the shop again, bought provisions, and came home. What was the total distance travelled, and his displacement from home?
2. 2A student runs from the ground floor to the 4th floor to fetch a book (3 m per floor), then comes down to the 2nd floor classroom. Find (i) total vertical distance, (ii) displacement from the start.
3. 3A girl riding a scooter sees a constant speedometer reading. Could her scooter still be accelerating? How?