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.
- v = u + at
- s = ut + \dfrac{1}{2}at^{2}
- 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.