Revise Kinematics for IB Physics (A.1)

To describe motion precisely we separate quantities that have only a size (scalars) from those that also have a direction (vectors). Distance and speed are scalars; displacement and velocity are vectors. In one dimension we capture direction with a sign: choose one direction as positive (say, to the right, or upwards) and the opposite direction is negative. The choice is yours, but once made it must be used consistently for every quantity in the problem.

The most common early error is treating distance and displacement (or speed and velocity) as interchangeable. They agree only when motion is in a single straight line without reversing. As soon as an object turns back on itself, the path length exceeds the magnitude of the displacement, and average speed exceeds the magnitude of the average velocity.

When acceleration is uniform (constant), four equations relate the five kinematic variables. They are known as the SUVAT equations after the symbols $s$, $u$, $v$, $a$, $t$. Each equation deliberately omits one of the five variables, and that is exactly what makes them useful: choose the equation that omits the variable you neither know nor want.

1. ; v = u + at
2. ; s = ut + \tfrac{1}{2}at^2
3. ; v^2 = u^2 + 2as
4. $\; s = \frac{(u+v)}{2}\,t$

Here $s$ is displacement, $u$ is initial velocity, $v$ is final velocity, $a$ is acceleration and $t$ is time. Equation 1 has no $s$; equation 2 has no $v$; equation 3 has no $t$; equation 4 has no $a$. Because these all assume constant acceleration, they must never be applied to a stage of motion where the acceleration is changing.

Graphs turn motion into a shape you can read at a glance, and two operations unlock them: the gradient (slope) and the area beneath the line. On a displacement–time graph the gradient is the velocity, so a straight line means constant velocity and a curve means acceleration; the steeper the line, the faster the object. On a velocity–time graph the gradient is the acceleration, and — crucially — the area under the line is the displacement. On an acceleration–time graph the area under the line is the change in velocity.

An object moving under gravity alone, with air resistance ignored, is in free fall — a perfect case of uniform acceleration. That acceleration is $g \approx 9.81$ m s⁻², directed downwards, and it is the same for all objects regardless of mass: a coin and a feather dropped in a vacuum land together. To handle free-fall problems, fix a sign convention. If you take upwards as positive, then for a ball thrown up the acceleration is $a = -g = -9.81$ m s⁻² throughout the motion — on the way up, at the top, and on the way down.

A projectile is any object moving under gravity alone in two dimensions — a ball thrown off a cliff, a kicked football, a stream of water. The key insight is that the horizontal and vertical motions are completely independent and share only the same clock. Horizontally there is no force (air resistance ignored), so the horizontal velocity is constant. Vertically the object is in free fall with acceleration $g$ downwards. You solve a projectile by analysing each direction with its own SUVAT list, connected only through the common time $t$.

Real objects falling through air or water experience fluid resistance (drag), a force that opposes motion and grows larger as the object moves faster. Release an object from rest and at first its weight far exceeds the drag, so it accelerates. As it speeds up the drag increases, the resultant downward force shrinks, and the acceleration falls. Eventually the upward drag grows to equal the weight: the resultant force is zero, the acceleration is zero, and the object continues at a constant speed — its terminal velocity. On a velocity–time graph this appears as a curve that rises steeply, then bends over and flattens into a horizontal line. Note that once drag matters, the acceleration is no longer constant, so the SUVAT equations no longer apply.

In Paper 2 the marks are analytic: each is tied to a specific line of working — a method mark (M) or an answer mark (A) — and error-carried-forward (ECF) means a wrong number early on does not have to cost you the marks that follow. But that protection only exists if your method is written down. Study how each mark below is earned by a specific line, especially in a projectile question where the vertical and horizontal parts are marked separately.

Kinematics describes motion; the next topics explain it. Once you can quantify velocity and acceleration, Newton's laws connect that acceleration to the forces that cause it, and the SUVAT toolkit reappears wherever acceleration is uniform. The graph skills carry straight into interpreting force–time and momentum problems, and the independence of components underlies all two-dimensional dynamics. Master the habit — list the variables, pick the equation that omits the unwanted one, keep components separate, show every line — and the mechanics that follows becomes variations on a method you already own.