Kinematics and Projectile Motion

Describing motion

• Displacement (s) — vector distance from the start.
• Velocity (v) — rate of change of displacement (vector).
• Acceleration (a) — rate of change of velocity (vector).

The SUVAT equations (uniform acceleration)

For constant acceleration in a straight line:

v = u + at
s = ut + ½at²
v² = u² + 2as
s = ½(u + v)t

where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time. List the known quantities and choose the equation with only one unknown.

Motion graphs

• Displacement–time: gradient = velocity.
• Velocity–time: gradient = acceleration; area under = displacement.
• Acceleration–time: area under = change in velocity.

Free fall

Near Earth, objects accelerate downward at g ≈ 9.81 m/s² (ignoring air resistance). Use SUVAT with a = g. Measuring g is a standard required practical (e.g. timing a falling object with light gates).

Projectile motion

A projectile has independent horizontal and vertical motions:

• Horizontal: constant velocity (no horizontal force, ignoring air resistance) → s = v_x t.
• Vertical: uniform acceleration g → use SUVAT with a = g.
• The two are linked only by the shared time t.

Method: resolve the launch velocity into horizontal (u cos θ) and vertical (u sin θ) components; analyse each direction separately.

Terminal velocity

With air resistance, a falling object accelerates until drag equals weight; the resultant force is zero and it falls at a constant terminal velocity.

Worked example

A ball is thrown horizontally at 5 m/s from a 20 m high cliff. How long until it lands? (g = 9.81)

• Vertical: s = ½gt² → 20 = ½ × 9.81 × t² → t² = 4.08 → t ≈ 2.0 s (horizontal speed doesn't affect the fall time). ✓

Common mistakes

• Mixing horizontal and vertical motions — treat them independently, linked only by time.
• Using SUVAT when acceleration is not constant.
• Sign errors — choose a positive direction and stick to it (e.g. down as negative).

Exam tips

• List s, u, v, a, t, mark the unknown, and pick the right SUVAT equation.
• For projectiles, resolve the initial velocity and analyse each direction separately.
• Read graphs correctly: v–t gradient = acceleration, area = displacement.

Key facts to remember

• SUVAT equations apply for constant acceleration; free fall uses a = g ≈ 9.81 m/s².
• Motion graphs: displacement–time gradient = velocity; velocity–time gradient = acceleration, area = displacement.
• Projectiles: independent horizontal (constant v) and vertical (a = g) motions, linked by time; terminal velocity when drag = weight.