Describing motion with vectors, graphs and equations
Kinematics describes how objects move without asking why. Position is measured from a chosen origin, displacement is the change in position, velocity is the rate of change of displacement and acceleration is the rate of change of velocity. For constant acceleration, the equations v = u + at, s = ut + ½at² and v² = u² + 2as connect these quantities. On a velocity–time graph, the slope gives acceleration and the area under the line gives displacement.
Motion in two dimensions is handled by splitting vectors into perpendicular components. A projectile launched with speed u at angle θ has a constant horizontal velocity u cos θ while its vertical motion is uniformly accelerated by gravity. Its time of flight is 2u sin θ/g, its maximum height is u² sin²θ/2g, and its range is u² sin 2θ/g, which is largest at 45°. Relative velocity, v_AB = v_A − v_B, explains problems like rain falling on a moving person or a boat crossing a river.
Why it matters
Kinematics is used to plan the path of a thrown ball, the landing point of a long jump, safe braking distances for vehicles and the trajectory of satellites and spacecraft. Reading slopes and areas on graphs is a skill used across physics, chemistry and economics. It is the foundation for Newton’s laws, work and energy, and rotational motion.
Key terms
- Displacement
- The straight-line change in position of an object, with both size and direction.
- Projectile
- An object thrown into the air that moves only under the influence of gravity.
- Range
- The horizontal distance covered by a projectile before it returns to its launch height.
- Relative velocity
- The velocity of one object as observed from another moving object.