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T3 PHYSICS SEMESTER EXAM

06/09/2025

Year 10 Semester 2 Physics FINAL Cheat Sheet

1. Motion Basics: Distance, Displacement, Speed, Velocity

  • Definitions:

    • Distance: Total path length (scalar, no direction). E.g., A to F path = sum of segments.
    • Displacement: Shortest straight-line from start to end (vector, with direction). Use Pythagoras for 2D: √(a² + b²).
    • Speed: Distance/time (scalar). Average speed = total distance/total time.
    • Velocity: Displacement/time (vector). Convert: 1 m/s = 3.6 km/h (multiply m/s by 3.6 for km/h; divide km/h by 3.6 for m/s).

  • Key Formulas:

    • Speed: v = d / t (or rearrange for d = v t, t = d / v).
    • Displacement (2D): Draw right triangle, c = √(a² + b²).

  • Tips for Calcs:

    • Always convert units (km to m: x1000; hours to sec: x3600).
    • Exam trick: If journey North 30m then East 80m, distance = 110m, displacement = √(30² + 80²) = 85.4m East of North.
    • Average speed: Total distance / total time (not average of speeds).

  • Graphs:

    • Distance-Time Graph: Slope = speed. Flat = stopped. Negative slope = returning.
    • Displacement-Time Graph: Slope = velocity. Can be negative (opposite direction).
    • Gradient: m = (y2 - y1) / (x2 - x1). Higher gradient = faster.

Quick Example: Person walks 80km in 6h: speed = 80/6 ≈ 13.33 km/h = (13330 m)/(21600 s) ≈ 0.62 m/s.

2. Acceleration & Velocity-Time Graphs

  • Definitions:

    • Acceleration: Change in velocity/time (a = (v - u)/t, where u = initial velocity, v = final).
    • Positive a = speeding up; negative = deceleration.
    • Terminal Velocity: Max speed when air resistance = gravity (a=0).
    • Gravity accel: g = 10 m/s² (downward).

  • Key Formulas:

    • a = (v - u) / t.
    • Final velocity: v = u + a t.
    • Convert accel: km/h/s to m/s²: divide by 3.6.
    • Distance from graph: Area under velocity-time curve (rectangle: l x w; triangle: ½ base x height; trapezium: ½ (a+b) h).

  • Velocity-Time Graph Tips:

    • Slope = acceleration (positive slope = accel, negative = decel, flat = constant velocity).
    • Area under graph = distance/displacement (subtract negative areas for displacement).
    • Exam trick: If speed from 20 to 80 km/h in 5s, a = (80-20)/5 = 12 km/h/s = 12/3.6 ≈ 3.33 m/s².

Quick Example: Car from 12 m/s to 46 m/s in 8s: a = (46-12)/8 = 4.25 m/s² = 4.25 x 3.6 ≈ 15.3 km/h/s. If continues 6s more: v = 46 + 4.25x6 ≈ 71.5 m/s.

3. Newton’s Laws & Forces

  • Definitions:

    • Force: Push/pull (vector, in Newtons, N). Net force (Fnet) = sum of forces (add same direction, subtract opposites).
    • Inertia: Resistance to motion change (more mass = more inertia).
    • Weight: Force due to gravity (W = m g, g=10).
    • Mass vs Weight: Mass (kg) constant; weight (N) changes with g (e.g., less on moon).

  • Newton’s Laws:

    • 1st (Inertia): Object at rest stays at rest, or constant velocity unless net force acts. (E.g., book flies forward in braking car).
    • 2nd: F = m a (accel proportional to force, inverse to mass). (E.g., small motorcycle accelerates faster than heavy bus with same force).
    • 3rd: Every action has equal/opposite reaction (on different objects). (E.g., rocket thrust: gas pushes back, rocket forward; both boys fly back when one pushes).

  • Key Formulas:

    • F = m a (rearrange: a = F/m, m = F/a).
    • Net force: Subtract opposing forces (e.g., push 350N right, friction 250N left: Fnet=100N right).
    • Weight: W = m x 10 (e.g., 65kg on Earth: 650N; on planet with 780N: a=780/65=12 m/s² > Earth’s).

  • Tips:

    • Balanced forces: a=0 (constant velocity or rest).
    • Unbalanced: Net force causes accel.
    • Exam trick: For 3500kg car a=40cm/s²=0.4m/s² left: F=3500x0.4=1400N left.
    • Friction/Reaction: Vertical reaction = weight (up); friction opposes motion.

Quick Example: Box 15kg, pushed 100N right, a=8 m/s²: Fnet=15x8=120N right (so friction=100-120? Wait, recheck: actually use Fnet = push - friction = m a).

4. Energy & Work

  • Definitions:

    • Work: Energy transferred by force over distance (W = F x s). If no movement, work=0.
    • Kinetic Energy (KE): Energy of motion (KE = ½ m v²).
    • Gravitational Potential Energy (GPE): Stored due to height (GPE = m g h, g=10).
    • Elastic Potential Energy: Stored in stretched/compressed objects (EPE = ½ k x², k=spring constant, x=stretch).
    • Conservation: Energy can’t be created/destroyed, only transformed (total E constant, minus losses like heat/sound).

  • Key Formulas:

    • Work = F x d = ΔEnergy.
    • KE = ½ m v².
    • GPE = m g h.
    • Total E = KE + GPE (constant in isolated system).
    • Efficiency = (useful output / total input) x 100% (e.g., winch does 200kJ but needed 120kJ: eff=60%).
    • Speed from energy: v = √(2 KE / m) or from fall: v = √(2 g h).

  • Tips:

    • Dropped object: GPE at top = KE at bottom (v=√(2gh)).
    • Rollercoaster: Max GPE at top, max KE at bottom. Total E same.
    • Exam trick: 10kg ball dropped from 5m: GPE=10x10x5=500J = KE at bottom, v=√(2x500/10)=√100=10 m/s.
    • Braking: ΔKE = work by brakes (negative work).

Quick Example: Car 2000kg at 80km/h=22.22 m/s: KE=½x2000x(22.22)²≈493827J. Slow to 20km/h=5.56 m/s: ΔKE negative, work=ΔKE.

5. Momentum & Collisions

  • Definitions:

    • Momentum (p): p = m v (vector). Conserved in isolated systems (total p before = after).
    • Isolated system: No external forces.

  • Key Formulas:

    • p = m v.
    • Conservation: m1 v1 + m2 v2 (before) = m1 v1’ + m2 v2’ (after).

  • Tips: Exam may derive from Newton’s laws. E.g., colliding trolleys: total p constant.

6. Graphs & Experiments

  • Independent Var: Changed (x-axis, e.g., ramp height).
  • Dependent Var: Measured (y-axis, e.g., speed).
  • Controlled: Kept same (e.g., mass).
  • Graph: Title, labels+units, consistent scale, line of best fit.
  • Exam trick: For elasticity vs range, table averages, plot elasticity (x) vs distance (y).

The Extended Response (The 12-Mark Question)

The exam will definitly have a question asking you to analyze experimental data.

1.  Identify Variables:

-   Independent Variable: What you change on purpose. Plot this on the X-axis.

-   Dependent Variable: What you measure as a result. Plot this on the Y-axis.

-   Controlled Variables: Everything else you keep the same to ensure a fair test.

2.  Draw a Data Table:

-   Give it a clear, descriptive title (e.g., “The Effect of [Independent Variable] on [Dependent Variable]”).

-   Use columns with clear headings and UNITS (e.g., “Elasticity (GPa)”, “Range (m)”).

-   If there are multiple trials, include a column for the average.

3.  Plot the Graph (TASP Method):

-   Title: Same descriptive title as your table.

-   Axes: Label both the X-axis (Independent Variable) and Y-axis (Dependent Variable) with their names and units.

-   Scale: Choose a consistent and sensible scale for both axes. It must start at 0 and go up in even steps.

-   Plot: Plot your average data points accurately. Use a small ‘x’ or a dot for each point.

Stuff To Remember!!

  • Show Working: Formula (1 mark), sub values (1), answer (1). Units!
  • Common Traps: Displacement ≠ distance; speed ≠ velocity; work only if moved.
  • Newton’s Laws Apps: 1st=why seatbelts; 2nd=heavy needs more F; 3rd=equal forces but different effects.
  • Energy: Always check conservation; ignore friction unless stated.
  • Graphs: Area=distance, slope=accel/speed.
  • Read question: Vectors need direction!
  • Time: Calcs first, explain with laws.