The full lecture — read the prose on the left while the live panel on the right shows each idea through an everyday object: a speedometer, a bus, a sprinter, a stone down a well, a cricket ball. Press ▶ and the narration walks you through, section by section.
1 — Speed & velocity
Mechanics studies motion; kinematics describes it without asking about forces. We begin with how fast and which way a body moves.
- Speed — the rate of change of distance. A scalar (size only). SI unit: metre per second (m/s).
- Velocity — the rate of change of displacement; speed in a stated direction. A vector. SI unit: m/s.
Definitionsaverage speed = total distance / total time
velocity = displacement / time (unit: m/s)
Speedometer point: a car dial reads only the speed. The moment you say "20 m/s heading north", you have given the velocity.
2 — Distance–time graphs
Plot distance (y-axis) against time (x-axis). The slope (gradient) of the line is the speed of the body.
| Graph shape | What it means |
|---|
| Horizontal line | at rest (speed = 0) |
| Straight sloping line | uniform (constant) speed |
| Curve getting steeper | speeding up (acceleration) |
average speed
A bus covers 240 m in 12 s. Find its average speed.
v = distance / time = 240 / 12 = 20 m/s
3 — Acceleration
- Acceleration — the rate of change of velocity. A vector, SI unit m/s².
Accelerationa = (v − u) / t
u = initial velocity · v = final velocity · t = time
Retardation (deceleration) is negative acceleration — the velocity is decreasing.
find a
A sprinter speeds up from 2 m/s to 10 m/s in 4 s.
a = (v − u)/t = (10 − 2)/4 = 2 m/s²
4 — Distance & displacement
- Distance — total length of the path actually walked. A scalar, always positive.
- Displacement — the shortest straight-line gap from start to finish, with direction. A vector.
SI unit & the 3–4–5 caseboth measured in metres (m)
√(3² + 4²) = √25 = 5 m → distance ≥ |displacement|
Exam point: walk a full lap of a circular track back to the start — your distance is the whole lap but your displacement is zero.
5 — Equations of motion
For straight-line motion with uniform acceleration, three equations connect the five quantities (u, v, a, t, S):
The three equations① v = u + a t
② S = u t + ½ a t²
③ 2 a S = v² − u²
Strategy: list which of u, v, a, t, S you know and which you want, then pick the equation that contains exactly those letters.
use equation ②
A car starts from rest and accelerates at 2 m/s² for 6 s. Find the distance.
u = 0, a = 2, t = 6
S = ut + ½at² = 0 + ½(2)(6²) = 36 m
6 — Velocity–time graphs
Plot velocity against time. Two powerful readings come straight off this graph:
Two key readingsslope of the line = acceleration (a)
area under the line = distance / displacement (S)
area = distance
A body accelerates from rest to 20 m/s in 10 s.
area = ½ × base × height = ½ × 10 × 20 = 100 m
7 — Motion under gravity (free fall)
Near the Earth's surface every freely-falling body accelerates downward at g ≈ 9.8 m/s² (often taken as 10 m/s² for quick work), the same for every mass. Replace a with g, and S with the height h.
Equations for free fallv = u + g t
h = u t + ½ g t²
2 g h = v² − u²
dropped from rest
A stone is dropped (u = 0) into a well and falls for 3 s. Take g = 10 m/s².
v = u + gt = 0 + 10(3) = 30 m/s
h = ½ g t² = ½(10)(3²) = 45 m
8 — Projectile motion & recap
- Projectile — a body given an initial velocity, then moving freely under gravity alone. Its path is a parabola.
It splits into two independent motions: a constant horizontal velocity, and a vertical motion accelerating at g.
Launched at speed u, angle θ (g down)Time of flight T = 2u sinθ / g
Max height H = u²sin²θ / 2g
Range R = u² sin2θ / g (max at θ = 45°)
- Speed (scalar) vs velocity (vector); distance vs displacement.
- Acceleration a = (v − u)/t, unit m/s².
- Graphs: slope & area readings.
- Three equations of motion; free fall (g); projectiles (max range at 45°).