Theme A · Space, Time and Motion · SL + HL · 9 hours

A.1 Kinematics

How can the position of a body in space and time be predicted?

Kinematics is the description of motion without asking why it happens. Before Newton's laws can tell you what a force does, you need the language to say what a body is doing: where it is, how fast it is moving, and how that motion is changing. This topic builds that language — position, displacement, velocity, and acceleration — and connects it to the four equations of motion that let you solve any problem where acceleration is constant.

The distinction between scalar and vector quantities runs through everything. Speed is a scalar; velocity is a vector. Distance is a scalar; displacement is a vector. The difference matters in two dimensions: a projectile launched at an angle has independent horizontal and vertical components, and the equations of motion are applied separately to each. Understanding this is the gateway to circular motion, orbital mechanics, and the more complex force problems in A.2.

A ball is launched horizontally from the edge of a cliff at 15 m s⁻¹. The cliff is 45 m high. Where does the ball land, and what is its speed at the moment of impact? (g = 9.8 m s⁻²)

What students must understand

Motion can be described in terms of position, velocity, and acceleration
Velocity is the rate of change of position; acceleration is the rate of change of velocity
Displacement is the change in position (a vector); distance is the total path length (a scalar)
The difference between instantaneous and average values of velocity, speed, and acceleration
The four kinematic equations for uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as, s = (u+v)/2 · t
Motion with uniform and non-uniform acceleration
Projectile motion (no fluid resistance): equations applied independently to horizontal and vertical components; trajectory is parabolic
The qualitative effect of fluid resistance on projectiles — trajectory, terminal speed, and how range changes

Guidance notes

Quantitative projectile problems are limited to situations where fluid resistance is absent or negligible
Projectiles launched horizontally, above the horizontal, and below the horizontal are all required
The equation of the parabolic trajectory is not required
Problems use a constant value of g near Earth's surface; g varies with altitude is Theme D territory

Linking questions

How does the motion of a mass in a gravitational field compare to a charged particle in an electric field? → D.1 Gravitational Fields, D.2 Electric and Magnetic Fields
How are the equations of rotational motion related to those for linear motion? → A.4 Rigid Body Mechanics
When can projectile problems be solved using energy conservation instead of kinematic equations? → A.3 Work, Energy and Power
How effectively do the equations of motion model Newton's laws? → A.2 Forces and Momentum
How does graphical analysis allow determination of other physical quantities? (NOS)