Physics Kinematics: Scalars, Vectors, and SUVAT Equations
Physical Quantities Reference
| Symbol | Quantity | SI Unit | Type |
|---|---|---|---|
| s | Displacement / Distance | m (meters) | Vector / Scalar |
| u | Initial Velocity | m/s (meters per second) | Vector |
| v | Final Velocity / Speed | m/s (meters per second) | Vector / Scalar |
| a | Acceleration | m/s² (meters per second squared) | Vector |
| t | Time | s (seconds) | Scalar |
| m | Mass | kg (kilograms) | Scalar |
| W | Weight | N (Newtons) | Vector |
| g | Gravitational Field Strength | 9.8 N/kg (or m/s²) | Vector |
1. Scalars vs. Vectors
- Scalar: A physical quantity that has magnitude (size) only, with no direction.
- Examples: Distance (15 m), Speed (25 m/s), Mass (60 kg), Time (12 s), Energy (400 J).
- Vector: A physical quantity that has both magnitude and direction.
- Examples: Displacement (15 m East), Velocity (25 m/s North), Acceleration (-9.8 m/s² downward), Weight / Force (588 N downward).
2. Speed, Velocity, and Acceleration
Speed
- Formula: Speed = Distance / Time
- Symbols: v = d / t
- Units: Distance in meters (m), Time in seconds (s), Speed in meters per second (m/s)
Velocity
- Formula: Velocity = Displacement / Time
- Symbols: v = s / t
- Units: Displacement in meters (m), Time in seconds (s), Velocity in meters per second (m/s)
Acceleration
Measures the rate of change of velocity over time.
- Formula: Acceleration = (Final Velocity – Initial Velocity) / Time
- Symbols: a = (v – u) / t
- Rearranged for Final Velocity: v = u + at
- Rearranged for Time: t = (v – u) / a
- Units: Acceleration in meters per second squared (m/s²), Velocity in m/s, Time in s
3. Velocity–Time (v–t) Graphs
- Gradient (Slope): Represents Acceleration.
- Gradient = (Change in Velocity) / (Change in Time) = (v – u) / t
- Area Under the Graph: Represents Total Distance (or Displacement).
Area Calculations
- Right-Angled Triangle (Constant acceleration from rest, or decelerating to rest):
- Area = (1/2) × Base × Height
- Distance = (1/2) × t × v
- Rectangle (Constant velocity):
- Area = Base × Height
- Distance = t × v
- Trapezium (Acceleration between two non-zero velocities):
- Area = (1/2) × (Sum of Parallel Sides) × Height
- Distance = [(u + v) / 2] × t
4. Core Kinematics Equations (SUVAT)
Use these when acceleration is constant:
- Equation 1 (No displacement s): v = u + at
- Equation 2 (No final velocity v): s = ut + (1/2)at²
- Equation 3 (No acceleration a): s = [(u + v) / 2] × t
- Equation 4 (No time t): v² = u² + 2as
- Rearrange for Displacement: s = (v² – u²) / (2a)
- Rearrange for Acceleration: a = (v² – u²) / (2s)
5. Weight, Mass, and Gravity
The Core Formula
- Formula: Weight = Mass × Gravitational Field Strength
- Symbols: W = m × g
- W = Weight in Newtons (N)
- m = Mass in kilograms (kg)
- g = Gravitational field strength on Earth = 9.8 N/kg (or 9.8 m/s²)
Rearrangements
- Mass: m = W / g
- Gravity: g = W / m
- Weight: W = m × g