Topic 1.3: Mechanics - Edexcel IAL Physics A-level

1.3.1 Equations of Motion

• Used when an object is moving at uniform acceleration.
• Key Formulas:
  • ( v = u + at )
  • ( s = ut + \frac{1}{2}at^2 )
  • ( v^2 = u^2 + 2as )
• Variables:
  • ( s ) = displacement
  • ( u ) = initial velocity
  • ( v ) = final velocity
  • ( a ) = acceleration
  • ( t ) = time
• Example problem: Stone dropped from a bridge.
  • Initial velocity ( u = 0 ), acceleration ( a = 9.81 \text{ m/s}^2 ).

1.3.2-3 Displacement, Velocity, and Acceleration-Time Graphs

• Distance: Scalar, total ground covered.
• Displacement ( s ): Vector, overall distance and direction from start.
• Speed: Scalar, rate of distance per unit time.
• Velocity ( v ): Vector, rate of change of displacement.
• Acceleration ( a ): Rate of change of velocity.
• Graphs:
  • Acceleration-time: Area under graph = change in velocity.
  • Velocity-time: Gradient = acceleration; Area = displacement.
  • Displacement-time: Gradient = velocity.

1.3.4 Scalars and Vectors

• Scalars: Only magnitude (e.g., distance, speed, mass).
• Vectors: Magnitude and direction (e.g., displacement, velocity, force).
• Vector representation: bold, underlined, or arrow notation.

1.3.5 Resolving Vectors

• Calculation: Use trigonometry to separate into components ( x = V\cos\theta ), ( y = V\sin\theta ).
• Scale Drawing: Use a ruler and protractor for graphical representation.

1.3.6 Adding Vectors

• Calculation: Use Pythagoras and trigonometry when vectors are perpendicular.
• Scale Drawing: For non-perpendicular vectors.

1.3.7 Projectile Motion

• Vertical and horizontal components evaluated separately.
• Use uniform acceleration formulas.
• Example: Ball projected at an angle, resolving initial speed into components.

1.3.8 Free-Body Force Diagrams

• Illustrates all forces on an object.
• Example: Car at constant velocity—forces balance.

1.3.9 Newton's Laws of Motion

• First Law: Object remains at rest or constant velocity without resultant force.
• Second Law: ( F = ma ); proportionality of acceleration to resultant force.
• Terminal Velocity: No resultant force; constant velocity.

1.3.10 Gravitational Field Strength and Weight

• Gravitational Field Strength ( g ): Force per unit mass.
• Weight ( W ): ( W = mg ); gravitational force on an object.

1.3.13 Momentum

• Momentum ( p ): Product of mass and velocity. ( p = mv ).
• Conservation: Momentum is conserved in isolated systems.
  • Example: Collision of car and truck.

1.3.15 Moments

• Moment: Force multiplied by perpendicular distance.
• Principle of Moments: Anticlockwise moments = clockwise moments in equilibrium.

1.3.17 Work

• Work Done ( W ): Force ( F ) times distance ( s ) in direction of force.
• Formula: ( W = Fs )

1.3.18 Kinetic Energy

• ( E_k = \frac{1}{2}mv^2 ): Energy of motion.

1.3.19 Gravitational Potential Energy

• ( E_{grav} = mgh ): Energy due to position in a field.

1.3.20 Conservation of Energy

• Energy cannot be created or destroyed; constant in a closed system.

1.3.21 Power

• Power ( P ): Rate of energy transfer, ( P = \frac{W}{t} ).

1.3.22 Efficiency

• Efficiency = ( \frac{\text{useful output}}{\text{total input}} ) as a measure of energy transfer effectiveness.