Kinematics

A-Level Physics 9702 · Topic 2 revision notes · AS

Motion described: displacement, velocity and acceleration, the graphs that link them, the SUVAT equations, free fall and projectiles.

8 definitions to learn word for word, 10 equations in their own column, 4 diagrams and graphs. Read it, cover it, test yourself.

Definitions (mark-scheme wording)EquationsExam traps

2.1aDescribing motion and motion graphs

Distance: the total length of path travelled (scalar).
Displacement: the distance in a straight line from a fixed point in a specified direction (vector).
Speed: the rate of change of distance (distance travelled per unit time).
Velocity: the rate of change of displacement.
Acceleration: the rate of change of velocity.

Displacement, velocity and acceleration are vectors: choose a positive direction and keep it.
s-t graph: gradient = velocity. A curve means changing velocity; take the gradient of the tangent.
v-t graph: gradient = acceleration, area under the line = displacement.
Area below the time axis on a v-t graph is displacement in the negative direction.
a-t graph: area = change in velocity.
Average velocity = total displacement / total time; instantaneous velocity = gradient at that instant.

s-t graph: steeper = faster; flat = at rest; the tangent gradient gives the instantaneous velocity.

v-t graph: gradient = acceleration, shaded area = displacement.

The gradient of a v-t graph is acceleration, but the area is displacement. Do not mix them up.
For a curved graph, the gradient at a point needs a tangent, not the line from the origin.

Uniform acceleration: acceleration that is constant in magnitude and direction.

Use SUVAT only when acceleration is constant.
Five quantities: s, u, v, a, t. Each equation leaves out one; pick the one without the quantity you neither know nor want.
List the three knowns and the one unknown before choosing an equation.
Decelerating object: a is negative (if forward is positive).
Derivation: a = (v - u)/t gives v = u + at; area under the v-t graph gives s = ½(u + v)t; combine for the other two.

Mixing sign conventions mid-question. Thrown up at u = +20 m s^-1 means a = -9.81 m s^-2 for the whole flight.
At the top of a vertical throw v = 0 but a = g (not zero).

Free fall: motion under gravity alone, with no air resistance; acceleration = g = 9.81 m s^-2 downwards.
Acceleration of free fall (g): the acceleration of a body falling freely in a uniform gravitational field.

Measuring g: drop a ball through heights s, time with light gates; plot s against t²: gradient = g/2.
Projectile: horizontal and vertical motions are independent; only the time is shared.
Horizontal: no force (air resistance ignored), so v_x = u cos θ stays constant.
Vertical: uniform acceleration g downwards, starting from u_y = u sin θ.
At maximum height v_y = 0; speed there = v_x.
Maximum range on level ground at θ = 45° (no air resistance).
With air resistance: lower height, shorter range, path no longer symmetrical.

Projectile: v_x is the same at every point; v_y falls to zero at the top, then grows downwards.

Measuring g: s against t² is a straight line through the origin with gradient g/2.

Never use the launch speed u in the horizontal and vertical equations at once. Resolve it first.
Gradient of s against t² is g/2, not g. Double it.