Motion – Quick Revision Notes

Reference Framework for Describing Motion

• Reference point / Origin: fixed point used to specify an object’s position.
• Motion: object changes position w.r.t. time.

Distance & Displacement

• Distance: total path length; scalar; always >0.
• Displacement: shortest straight-line from start to finish; vector.
  • Symbol: \Delta x = xf - x0
  • Can be +, - or 0 (zero when start = finish).
• Key differences
  • Distance gives complete path, not unique.
  • Displacement unique, direction-aware.

Scalars vs Vectors

• Scalar: magnitude only (distance, speed, time, mass).
• Vector: magnitude & direction (displacement, velocity, acceleration).

Types of Motion

• Uniform motion: equal distances in equal time intervals.
• Non-uniform motion: unequal distances in equal time intervals.

Speed & Velocity

• Speed: rate of distance change.
  • \text{speed} = \dfrac{\text{distance}}{\text{time}}, unit \text{m\,s^{-1}}.
  • Average speed = \dfrac{\text{total distance}}{\text{total time}}.
• Velocity: speed in a stated direction.
  • v = \dfrac{\text{displacement}}{t}, vector, unit \text{m\,s^{-1}}.
  • Average velocity (uniform) = \dfrac{u+v}{2}.
  • Average velocity (general) = \dfrac{\text{total }\Delta x}{\text{total }t}.
• Instantaneous speed / velocity: value at a specific instant.

Acceleration

• Rate of change of velocity: a = \dfrac{\Delta v}{t}; unit \text{m\,s^{-2}}.
• Uniform acceleration: equal \Delta v in equal t.
• Non-uniform acceleration: unequal \Delta v in equal t.
• Positive a: velocity increases; negative a (retardation): velocity decreases.

Graphical Representation

• Distance–time graph
  • Stationary: horizontal line.
  • Uniform motion: straight sloping line (constant gradient).
  • Non-uniform: curved/variable gradient.
• Velocity–time graph
  • Constant velocity: horizontal line.
  • Uniform acceleration: straight sloping line; area under line gives distance s.
  – Rectangle + triangle areas often used.
  • Non-uniform acceleration: curved line; area still equals s.

Equations of Motion (uniform straight-line acceleration)

1. v = u + at
2. s = ut + \dfrac{1}{2}at^{2}
3. v^{2} = u^{2} + 2as
   ( u: initial velocity, v: final velocity, a: uniform acceleration, t: time, s: displacement )

Circular Motion

• Uniform circular motion: constant speed along circle; velocity direction continually changes ⇒ accelerated motion.
• Velocity magnitude: v = \dfrac{2\pi r}{t} ( r: radius, t: period ).
• Examples: planets orbiting Sun, satellites in orbit.