Educerie · IB Diploma · Physics

Theme A — Space, time and motion

Theme A is mechanics: describing motion, explaining what causes it to change, and tracking the two quantities that are conserved along the way. Almost everything else in the course borrows from it.

A.1 Kinematics — describing motion

Distance is how far you travelled; displacement is how far you ended up from where you started, with a direction. Speed is a scalar, velocity a vector. A runner completing a 400 m lap has a distance of 400 m and a displacement of zero — and therefore an average velocity of zero, however fast they ran.

The suvat equations apply only when acceleration is constant:

v = u + at
s = ut + ½at²
v² = u² + 2as
s = ((u + v)/2) t

Choosing between them is a matter of spotting which quantity is missing from the question; the equation that does not contain it is the one to use.

Graphs are the other half of kinematics, and questions about them are worth more marks than the algebra:

• On a displacement–time graph, the gradient is velocity.
• On a velocity–time graph, the gradient is acceleration and the area under the line is displacement.
• On an acceleration–time graph, the area is the change in velocity.

Area below the axis is negative and must be subtracted — a body that goes out and comes back has a displacement smaller than its distance, and the graph shows exactly that.

Projectile motion works because the horizontal and vertical components are independent. Split the initial velocity into u cos θ horizontally and u sin θ vertically, then treat the horizontal motion as constant velocity and the vertical as constant acceleration g downward. Time is the only quantity the two share — which is why finding the time of flight from the vertical motion is almost always the first step.

Ignoring air resistance, the trajectory is a parabola. With air resistance the range and maximum height both fall, and the path becomes asymmetric, descending more steeply than it rose.

A.2 Forces and momentum

Newton's laws, stated as the scheme wants them:

1. A body remains at rest or moves with constant velocity unless acted on by a resultant force.
2. The resultant force equals the rate of change of momentum; for constant mass, F = ma.
3. If body A exerts a force on body B, then B exerts an equal and opposite force on A.

The third law is the one most often stated wrongly. The two forces act on different bodies — that is the whole content of the law. Two forces acting on the same body, such as a book's weight and the normal force from a table, are not a third-law pair; they are balanced forces, which is the first law. Getting this distinction right is a reliable mark.

Free-body diagrams solve most force problems. Draw the single body, mark every force acting on it as an arrow from the body, resolve into convenient perpendicular directions — for an inclined plane, along and perpendicular to the slope — and apply F = ma in each direction.

On an incline of angle θ, the component of weight along the slope is mg sin θ and the component perpendicular to it is mg cos θ. Swapping the sine and cosine is the standard error; check by taking θ → 0, where the slope component should vanish.

Momentum is p = mv, a vector. Impulse is FΔt = Δp, which is why a longer collision time means a smaller force for the same change in momentum — the physics behind crumple zones, airbags and bending your knees on landing.

Conservation of momentum: in the absence of external forces, total momentum before a collision equals total momentum after. This holds in every collision, elastic or not.

• Elastic — kinetic energy is also conserved.
• Inelastic — kinetic energy is not conserved; some becomes internal energy and sound. Momentum still is.

Define a positive direction before writing the equation, and give any object moving the other way a negative velocity. Nearly every wrong answer in this section is a sign error.

A.3 Work, energy and power

Work is W = Fs cos θ, where θ is the angle between the force and the displacement. The cosine matters: a force perpendicular to the motion does no work, which is why the tension in a string does no work on a mass in circular motion, and why carrying a bag horizontally does no work against gravity.

• Kinetic energy Ek = ½mv² — note the square. Doubling the speed quadruples the kinetic energy, and quadruples the braking distance.
• Gravitational potential energy ΔEp = mgΔh near a planet's surface. Only the change in height matters; where you put the zero is your choice.
• Elastic potential energy Ee = ½kx² for a spring obeying Hooke's law.

Conservation of energy is the most powerful tool in the theme. Many questions that look hopeless as force problems become one line as energy problems: a ball released from height h on a frictionless track arrives at the bottom with ½mv² = mgh, whatever the shape of the track.

Power is P = W/t, and also P = Fv for a constant force — the form to reach for when a question gives you a driving force and a steady speed.

Efficiency = useful output ÷ total input, as a fraction or percentage. It is never greater than 1; an answer above 100% means you have inverted the ratio.

Higher level extensions

Higher level adds rigid body mechanics — torque, moment of inertia, angular acceleration and angular momentum, which mirror the linear quantities one for one — and special relativity, covering reference frames, time dilation, length contraction and the invariance of the speed of light.

What actually loses marks in this theme

1. Using a suvat equation when acceleration is not constant.
2. Confusing distance with displacement, or speed with velocity.
3. Taking the gradient of a velocity–time graph when the question wanted the area.
4. Forgetting that area below the axis is negative.
5. Swapping sin θ and cos θ on an inclined plane.
6. Naming two forces on the same body as a Newton's third law pair.
7. Sign errors in momentum problems, from not defining a positive direction.
8. Asserting kinetic energy is conserved in an inelastic collision. Momentum is; energy is not.
9. Omitting units, or failing to convert km to m and g to kg.

Educerie · written from the published IB syllabus structure for Physics Theme A, first assessment 2025. Original text; equations quoted appear in the IB physics data booklet. Last reviewed 5 September 2026.