Chapter Overview
- Four suvat equations can be used in vector form for 2D motion — time stays a scalar.
- v² = u² + 2as cannot be used in vector form — apply it component-by-component instead.
- Split every vector into its i (horizontal) and j (vertical) components and solve each separately, or keep them in vector form.
- "Travelling parallel to a vector" means velocity is a scalar multiple of that vector — one component of velocity equals zero.
- For speed or distance, find the magnitude of the velocity or displacement vector using Pythagoras.
- Position from origin: r = r₀ + s where r₀ is the initial position and s is the displacement from start.
The Four suvat Equations in Vector Form
In 1D mechanics you used suvat equations with scalars. In 2D, exactly the same equations work — but now s, u, v, and a are vectors. Time, t, is still just a number (a scalar).
Think of it this way: if the 1D equation v = u + at works along one direction, it works along any direction simultaneously, as long as acceleration is constant. Vectors package the i and j directions into one neat expression.
Key pattern: any three of {s, u, v, a, t} lets you find the fourth. The method is identical to 1D — the only difference is that s, u, v, and a are now 2D vectors.
Practice Question 1
A particle starts with velocity (2i + 5j) ms⁻¹ and has constant acceleration (0.5i − 1j) ms⁻². Find its velocity after 4 seconds.
The One Equation That Doesn't Work Vectorially
The formula v² = u² + 2as involves squaring velocity and speed terms. Squaring a vector is not defined in the same way as squaring a number — so this formula cannot be applied to whole 2D vectors.
Instead, apply this equation separately to the i and j components:
vx² = ux² + 2axsxi-components only
vy² = uy² + 2aysyj-components only
Common trap: students try to "square the vector" or mix components. Always split this specific equation into two separate scalar equations — one per component.
Position Vector Formula
In many exam questions the particle has an initial position that is not the origin. The suvat equations give you the displacement s from the starting point, not from the origin. To get the full position vector r from the origin:
Analogy: imagine you start at grid reference (3, 5) on a map and walk 10 m east and 4 m north. Your displacement s = 10i + 4j, but your position is (13i + 9j). The origin of the map didn't move — you did.
If the question says "find the position vector at time t," you almost certainly need r = r₀ + s. If it says "find the displacement," s on its own is sufficient.
Practice Question 2
(10i − 3j) m
(1i + 4j) ms⁻¹
position vector after 5 seconds
How to Use the 2D suvat Equations
Finding Speed and Distance (Magnitudes)