Kinematics
Describing motion purely with mathematics — no forces involved yet.
Scalars have magnitude only: distance, speed, time, mass, temperature. Vectors have both magnitude and direction: displacement, velocity, acceleration, force. When solving problems, always check whether a quantity is a scalar or vector — this determines whether you can simply add values or must account for direction.
Uniform motion (eenparige beweging) means constant velocity: acceleration = 0. The x–t graph is a straight line (slope = velocity). The v–t graph is a horizontal line. No net force is required to maintain this state (Newton's 1st Law). Example: a car cruising at constant speed on a straight road.
Constant acceleration means the velocity changes by the same amount each second. The x–t graph is a parabola (curved). The v–t graph is a straight line (slope = acceleration). The four SUVAT equations link displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t). Any three known quantities let you find the other two.
A projectile launched horizontally has two independent motions: horizontal — constant velocity (no acceleration, air resistance ignored); vertical — free fall with g = 9.81 m/s² downward. Treat each axis separately using the same time t. Horizontal: x = v₀t. Vertical: y = ½gt². The actual path is a parabola.
Free fall is a special case of UAM where the only acceleration is g = 9.81 m/s² downward (on Earth). In the absence of air resistance, all objects fall with the same acceleration regardless of mass. At the top of the trajectory, velocity = 0 but acceleration = g still acts downward.
The velocity of A relative to B is: v_A/B = v_A − v_B. This is a vector subtraction. Example: if a train moves at 30 m/s east and a car moves at 20 m/s east, the train's velocity relative to the car = 30 − 20 = 10 m/s east. If they move in opposite directions, the relative speed is the sum of the magnitudes.
When launched at angle θ above horizontal with speed v₀, decompose: Horizontal: v_x = v₀cosθ (constant throughout). Vertical: v_y = v₀sinθ − gt (changes). Time to max height: t_top = v₀sinθ/g (set v_y = 0). Maximum height: H = (v₀sinθ)²/(2g). Horizontal range (flat ground): R = v₀²sin(2θ)/g. Range is maximum at θ = 45°. Complementary angles give equal ranges (e.g. 30° = 60°). At any point: total speed v = √(v_x² + v_y²). At the top: v_y = 0, so speed = v_x = v₀cosθ.
x–t graph: slope = velocity; straight line = constant v; curve = acceleration; horizontal = at rest. v–t graph: slope = acceleration; area = displacement; horizontal = constant v (a=0); straight diagonal = UAM. a–t graph: area = change in velocity; horizontal line = constant a (UAM); at zero = constant velocity. Examiner tip: always state units on graph axes, and use the word 'slope' not 'gradient' in IB/school contexts — both are acceptable. If v–t graph has a negative slope, the object decelerates (or accelerates in the negative direction).
x–t Graph (Position vs. Time)
slope: Slope = velocity (m/s)Shows how position changes over time. A straight line means constant velocity (uniform motion). A curve (parabola) means acceleration. The steeper the slope, the faster the object moves.
v–t Graph (Velocity vs. Time)
slope: Slope = acceleration (m/s²)area: Area = displacement (m)Shows how velocity changes over time. A straight line means constant acceleration (UAM). A horizontal line means zero acceleration. The area under the curve equals displacement.
a–t Graph (Acceleration vs. Time)
area: Area = change in velocity (m/s)For UAM, this is a horizontal line (constant a). The area under the a–t graph equals the change in velocity.
The acceleration 'a' in every kinematic formula is produced by a net force via F = ma. Read the v–t slope to find acceleration, then use F = ma to find the force — or vice versa.
💡Exam tip: Draw the v–t graph first. Slope = acceleration. Then apply F = ma.
Click any formula to see symbol definitions.
All formulas for this topic are in BINAS BINAS 35A1 & 35A2. In the exam you don't need to memorise the equations — but you must know which table to open and what every symbol means.