Revise Equations of motion for Cambridge 9702 (2.1)

In physics, how we describe movement matters. Displacement ($s$) is a vector quantity, telling you the straight-line change in position from start to end, including direction. Velocity ($v$) is also a vector; it's the rate at which displacement changes. Acceleration ($a$), another vector, is the rate at which velocity changes. Always consider the direction for these quantities!

Velocity: $v = \frac{\Delta s}{\Delta t}$ Acceleration: $a = \frac{\Delta v}{\Delta t}$

When an object moves with uniform (constant) acceleration, we can use a set of four powerful equations to link its motion variables. These are commonly known as the SUVAT equations, named after the quantities they relate: displacement ($s$), initial velocity ($u$), final velocity ($v$), acceleration ($a$), and time ($t$). Mastering these is crucial for exam success.

$v = u + at$ $s = \frac{1}{2}(u+v)t$ $s = ut + \frac{1}{2}at^2$ $v^2 = u^2 + 2as$

A common scenario for uniform acceleration is objects moving under gravity. Near Earth's surface, the acceleration due to gravity ($g$) is approximately $9.81 \, \text{m/s}^2$ downwards. This value is constant for objects in free fall (ignoring air resistance) and is crucial in many problems.

Graphs provide a powerful visual representation of motion. A displacement-time graph shows an object's position over time, where its gradient reveals the object's velocity. A velocity-time graph illustrates how velocity changes over time; here, the gradient gives the acceleration, and the area under the graph provides the total displacement. Curved lines on a velocity-time graph indicate non-uniform acceleration.

When an object, like a thrown ball, moves in two dimensions (e.g., horizontally and vertically), we call this projectile motion. The key insight here is that the horizontal and vertical components of motion are entirely independent of each other. This means you can apply the SUVAT equations separately to each direction. To do this, you first resolve the initial velocity into its horizontal and vertical components using trigonometry.

$u_x = u \cos(\theta) \quad \text{(Horizontal component)}$ $u_y = u \sin(\theta) \quad \text{(Vertical component)}$