Chapter 1: Describing Motion

Key Definitions

Distance: Total length of the path travelled (scalar). Symbol: d. Unit: metres (m).

Displacement: Distance travelled in a specific direction (vector). Symbol: s or x. Unit: metres (m).

Speed: Rate of change of distance (scalar). Symbol: v. Unit: m s⁻¹.

Velocity: Rate of change of displacement (vector). Symbol: v. Unit: m s⁻¹.

Average Speed = total distance / total time

Average Velocity = change in displacement / time taken → v = Δs / Δt

Scalar vs Vector Quantities

Scalar Quantities (Magnitude only) Vector Quantities (Magnitude & Direction)
Distance Displacement
Speed Velocity
Mass Acceleration
Time Force

Graphs of Motion

Displacement-Time Graph

Gradient = Velocity

The slope of the graph indicates the velocity

Example: Calculating Velocity from s-t Graph

If a displacement-time graph shows an object moves from 2m to 8m in 3 seconds:

Velocity = (8 - 2) / 3 = 2 m/s

Measuring Speed in the Laboratory

  • Two Light Gates: Measure time (Δt) to travel a fixed distance (Δs)
  • One Light Gate: Measure time (Δt) for an object of known length (l) to pass
  • Ticker-Timer: Dots on tape are made at regular intervals (e.g., 0.02 s)
  • Motion Sensor: Uses ultrasound pulses to calculate distance

Tip:

When using ticker-tape, evenly spaced dots indicate constant velocity, while increasing spacing shows acceleration.

Combining Vectors

Vectors are added by placing them "tip-to-tail". The resultant is the vector from the start of the first to the end of the last.

For perpendicular vectors, use Pythagoras' Theorem:

Resultant magnitude R = √(A² + B²)

Direction θ = tan⁻¹(opposite/adjacent)

Chapter 2: Accelerated Motion

Acceleration

Definition: The rate of change of velocity. It is a vector.

Symbol: a. Unit: m s⁻².

a = (v - u) / t or a = Δv / Δt

Remember:

Deceleration is simply negative acceleration. When an object slows down, its acceleration value is negative.

Velocity-Time Graphs

Velocity-Time Graph

Gradient = Acceleration, Area = Displacement

The slope gives acceleration, and the area under the graph gives displacement

Example: Calculating Acceleration from v-t Graph

If velocity increases from 4 m/s to 12 m/s in 4 seconds:

Acceleration = (12 - 4) / 4 = 2 m/s²

Equations of Motion (SUVAT Equations)

For objects moving in a straight line with constant acceleration:

v = u + at

s = ((u + v)/2) × t

s = ut + ½at²

v² = u² + 2as

SUVAT Reminder:

s = displacement, u = initial velocity, v = final velocity, a = acceleration, t = time

Acceleration Due to Gravity (g)

All objects in free fall (with no air resistance) accelerate at the same rate:

g = 9.81 m s⁻² (directed downward)

Example: Free Fall Calculation

How far does an object fall in 3 seconds from rest?

s = ut + ½at² = 0 + ½(9.81)(3)² = 44.145 m

Projectile Motion

A projectile's motion can be split into independent horizontal and vertical components:

  • Horizontal Motion: No acceleration (constant velocity)
  • Vertical Motion: Constant acceleration downward (g = -9.81 m/s²)
  • The path is a parabola

Horizontal component: vₕ = u cos θ

Vertical component: vᵥ = u sin θ

Example: Projectile Motion

A ball is kicked with initial velocity 20 m/s at 30° to the horizontal.

Horizontal component: 20 × cos(30°) = 17.32 m/s

Vertical component: 20 × sin(30°) = 10 m/s