P5.4 Forces and Motion
Key definitions
| Quantity | Definition | Symbol | Unit |
|---|---|---|---|
| Distance | Total path length | d | m |
| Displacement | Straight-line distance from start to finish (with direction) | s | m |
| Speed | Distance / time (scalar) | v | m/s |
| Velocity | Displacement / time (vector) | v | m/s |
| Acceleration | Change in velocity / time | a | m/s² |
Speed and velocity equations
v = d/t (speed) or v = s/t (velocity = displacement/time)
Typical speeds (approx.):
- Walking: 1.5 m/s
- Cycling: 6 m/s
- Car on motorway: 30 m/s
- Sound in air: 340 m/s
Acceleration
a = (v − u) / t
a = acceleration (m/s²), v = final velocity (m/s), u = initial velocity (m/s), t = time (s)
Rearranged: v = u + at.
Deceleration = negative acceleration.
Another kinematic equation (GCSE):
v² = u² + 2as
s = ut + ½at² (Higher)
Newton's Laws of Motion
Newton's First Law: An object remains at rest or moves at constant velocity unless acted on by a resultant force.
Newton's Second Law:
F = ma
F = resultant force (N), m = mass (kg), a = acceleration (m/s²)
Newton's Third Law: Every force has an equal and opposite reaction force (acting on a different object).
Distance–time and velocity–time graphs
Distance–time (d–t) graph:
- Gradient = speed
- Flat line = stationary
- Straight diagonal = constant speed
- Curve = changing speed (acceleration/deceleration)
Velocity–time (v–t) graph:
- Gradient = acceleration
- Area under graph = distance travelled
- Flat line = constant velocity
- Straight diagonal = constant acceleration/deceleration
Stopping distance
Stopping distance = Thinking distance + Braking distance
- Thinking distance = distance travelled during driver's reaction time (typically 0.2–0.9 s)
- Factors: tiredness, alcohol/drugs, distractions
- Braking distance = distance travelled while brakes applied
- Factors: speed, road condition (wet/icy), tyre quality, brake condition, mass of vehicle
✦Worked example— Worked example — Newton's 2nd Law
A 1,200 kg car accelerates at 3 m/s².
F = ma = 1200 × 3 = 3,600 N
✦Worked example— Worked example — kinematics
A ball rolls at 5 m/s and decelerates at 2 m/s². How far does it travel before stopping?
v² = u² + 2as → 0 = 25 + 2(−2)s → 4s = 25 → s = 6.25 m
Common exam errors
- Confusing mass (kg) and force (N) in F = ma.
- Reading the area under a velocity–time graph incorrectly (remember: ½ × base × height for triangles).
- Stating speed and velocity interchangeably — velocity requires direction.
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