Motion, Forces & Energy
Kinematics, Newton, momentum, moments, pressure and the energy chain, roughly a third of the paper and the section where units decide the grade.
Scalars, vectors, and why the paper cares
A scalar has size only: distance, speed, mass, energy, time. A vector has size and direction: displacement, velocity, acceleration, force, momentum, weight. The distinction is examined directly, and it matters for a second reason, vectors can cancel. Two 5 N forces in opposite directions give a resultant of zero; two 5 N forces at right angles give √50 ≈ 7.1 N by Pythagoras, or by a scale drawing.
Speed = distance ÷ time. Acceleration = change in velocity ÷ time. Both are given on the formula sheet; both are lost by students who mix units. Convert to metres and seconds before you start, and write the unit on every line. A speed of 72 km/h is 20 m/s; the examiner will not convert it for you.
Free fall near Earth: g ≈ 10 m/s² (the paper says 9.8 or 10. Use what it gives). It is an acceleration, so a dropped object gains 10 m/s of speed every second, regardless of its mass, until air resistance matters.
Motion graphs, three things to read off
A distance–time graph: gradient is speed. Flat is stationary. Curving up means speeding up.
A speed–time graph carries more, and is the one the paper prefers. Gradient is acceleration (negative when slowing). Area under the graph is distance. A flat section is constant speed, not stopped. That confusion costs marks every year.
Finding area: break it into rectangles and triangles. A car accelerating from 0 to 20 m/s in 4 s then holding 20 m/s for 6 s has travelled ½ × 4 × 20 + 6 × 20 = 40 + 120 = 160 m. Show the split; method marks live there.
Forces: F = ma, and the balanced-versus-unbalanced test
Resultant force = mass × acceleration. If the forces balance, resultant is zero, acceleration is zero, the object is stationary or moving at constant velocity. Both. Newton's first law does not say things stop; it says they do not change.
The classic explain-why: a skydiver. Weight is constant. Air resistance rises with speed. At first weight wins and she accelerates; as she speeds up, air resistance grows until it equals weight; resultant is then zero, acceleration is zero, and she falls at a steady terminal velocity. Open the parachute: air resistance jumps above weight, resultant is upward, she decelerates to a new, lower terminal velocity. Every sentence of that paragraph is a mark.
Weight = mg, in newtons. Mass in kg does not change on the Moon; weight does, because g does. Friction opposes motion and turns kinetic energy into thermal energy. Say "thermal", not "heat is lost".
Momentum, moments, pressure, three formulas, three traps
Momentum = mv, unit kg m/s, a vector. It is conserved in collisions: total before = total after. A 4 kg trolley at 6 m/s hitting a stationary 2 kg trolley and sticking: 24 = 6 × v, so v = 4 m/s. Force is rate of change of momentum: F = Δp ÷ t. That is why crumple zones work, same momentum change over a longer time means a smaller force.
Moment = force × perpendicular distance from the pivot, unit N m. Balanced when clockwise moments = anticlockwise moments. The trap is "perpendicular": a force applied along the line of the lever has no moment at all. A uniform beam's weight acts at its centre, include it when the pivot is not at the middle.
Pressure = force ÷ area, unit Pa = N/m². Small area, big pressure: the pin, the stiletto, the knife edge. In a liquid, p = ρgh: depends on depth, not on the shape or width of the container.
Energy: stores, transfers, and the two calculations
Energy is conserved: never created or destroyed, only transferred between stores. The stores you must name: kinetic, gravitational potential, elastic potential, chemical, thermal, nuclear, electrostatic. The transfers: mechanical work, electrical work, heating, radiation.
KE = ½mv². The v is squared: doubling speed quadruples kinetic energy, which is exactly why braking distance quadruples too. GPE = mgh. A pendulum swaps the two: at the bottom, all the GPE it lost has become KE (ignoring air resistance), so ½mv² = mgh and the m cancels.
Work done = force × distance moved in the direction of the force, and it equals the energy transferred. Power = work ÷ time, in watts. Efficiency = useful output ÷ total input, as a fraction or percentage, never above 100%. The wasted part is almost always thermal energy to the surroundings. Say so.
Where marks go
- "Constant velocity means a resultant force is keeping it going." No, constant velocity means resultant force is zero. The engine force balances friction.
- Flat section on a speed–time graph read as stationary. It is constant speed. Stationary is the axis.
- Mass and weight swapped. Mass is kg, weight is N, weight = mg.
- Distance on a speed–time graph read from the y-axis. It is the area.
- Moments with the wrong distance. Perpendicular distance from the pivot, not from the end of the beam.
- "Energy is used up." It is transferred, usually to a thermal store. The word "lost" is acceptable only with "to the surroundings".
- Units missing or wrong. A numerical answer without a unit is not a final answer.
What to remember
- Vectors have direction and can cancel; scalars cannot.
- Speed–time graph: gradient = acceleration, area = distance.
- F = ma. Zero resultant means constant velocity, not necessarily rest.
- Terminal velocity: air resistance has grown to equal weight.
- Momentum mv is conserved. Moment = F × perpendicular d. Pressure = F ÷ A, and p = ρgh in liquids.
- KE = ½mv², GPE = mgh, W = Fd, P = W/t. Efficiency is never over 100%.
- SI units on every line: m, s, kg, N, J, W, Pa.
Watch one worked through
Here is one done slowly, with the reason for every move. Then one for you.
A car accelerates from rest to 20 m/s in 8 s. Its mass is 1200 kg. Find the acceleration, the resultant force and the kinetic energy at 20 m/s.
- Acceleration is change in velocity over time.a = (20 − 0) ÷ 8 = 2.5 m/s²Use the change in velocity, not the final value. Starting from rest makes them equal here, which hides the error for later questions.
- Apply Newton's second law.F = ma = 1200 × 2.5 = 3000 NThis is the resultant force, the leftover after friction and drag. It is not the force the engine produces.
- Use the kinetic energy formula.KE = ½mv² = ½ × 1200 × 20²Only the velocity is squared, not the mass. Squaring both is a frequent and expensive slip.
- Evaluate.= 0.5 × 1200 × 400 = 240 000 J = 240 kJBecause v is squared, doubling the speed quadruples the energy. That is why stopping distances grow so fast with speed.
Answer: 2.5 m/s², 3000 N and 240 kJ
What is the kinetic energy of a 2 kg object moving at 3 m/s, in joules?
Show the answer
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