Physics · Lesson 3

Motion: the SUVAT toolkit

JAMBWAECNECO

What the syllabus asks

JAMB: Motion: scalars and vectors, linear motion, equations of motion, free fall

WAEC: Motion: types of motion, speed, velocity, acceleration, distance–time and velocity–time graphs, equations of uniformly accelerated motion, motion under gravity, projectiles (introductory)

NECO: Motion: types of motion, speed, velocity, acceleration, distance–time and velocity–time graphs, equations of uniformly accelerated motion, motion under gravity, projectiles (introductory)

What you will learn

Distinguish scalars from vectors and distance from displacement.
Calculate speed, velocity and acceleration.
Interpret distance–time and velocity–time graphs (slope and area).
Derive and apply the equations of uniformly accelerated motion.
Solve free-fall problems using g.
Analyse simple horizontal projectiles.

Key points

Scalars have magnitude only; vectors also have direction (displacement, velocity, acceleration).
Average speed = total distance/total time; a = (v − u)/t.
s–t graph: slope = speed. v–t graph: slope = acceleration and area = distance.
SUVAT: v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u + v)t (constant a only).
Free fall: a = g ≈ 10 m/s²; H = u²/2g; time up = u/g.
Horizontal projectile: x = ut, y = ½gt²; the time depends only on the height.
Ticker tape (50 Hz): 1 tick = 0.02 s; spacing shows the type of motion.
Resultant of perpendicular vectors: size √(a² + b²), direction from tan θ = opposite/adjacent; components are v cos θ and v sin θ.
Stopping distance = thinking distance (speed × reaction time) + braking distance (u²/2a).
Terminal velocity is reached when drag equals weight, so the resultant force and acceleration become zero.

Start here: Types of motion; scalars and vectors

Look around a Nigerian motor park and you will see every kind of motion. A danfo moves along the road (translational, or linear, motion). Its wheels spin (rotational). The engine's pistons go up and down (oscillatory, or vibratory). The dust and smoke particles jiggle about at random (random motion). WAEC asks you to name and give examples of these four types.

To describe motion with numbers, we need two kinds of quantity.

Scalar: has size (magnitude) only, such as distance, speed, mass, time and energy.
Vector: has size AND direction, such as displacement, velocity, acceleration, force and momentum.

Here is why direction matters. Ada walks 300 m east from her house to a shop, then 300 m back west. She has walked a distance of 600 m, but her displacement is zero, because she ends where she started.

Figure 3.1: Distance 600 m; displacement 0.

Worked example 3.1

A boy walks 8 m north and then 6 m east. Find (a) the distance and (b) the displacement.

(a) Distance = 8 + 6 = 14 m.
(b) The path makes a right-angled triangle. Displacement = √(8² + 6²) = √100 = 10 m.
Direction: tan θ = 6/8, so θ ≈ 36.9° east of north.

14 m; 10 m at N36.9°E

⚠️ Common mistake: adding vectors like ordinary numbers. 8 m north plus 6 m east is NOT 14 m of displacement.

Try it yourself. An athlete runs one full lap of a 400 m track. State the distance and the displacement.

Show solution

Distance 400 m; displacement 0 (back at the start).

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Practice questions

1. Convert 54 km/h to m/s.

Show worked answer

15 m/s.

2. A car accelerates from 5 m/s to 25 m/s in 8 s. Find a and the distance covered.

Show worked answer

a = 2.5 m/s²; s = ½(5 + 25) × 8 = 120 m.

3. A ball is thrown up at 15 m/s. Find the maximum height (g = 10).

Show worked answer

225/20 = 11.25 m.

4. A body decelerates from 20 m/s to rest over 50 m. Find the deceleration.

Show worked answer

0 = 400 − 100a, so a = 4 m/s².

5. A stone is thrown horizontally at 12 m/s from a 45 m cliff. Find the range.

Show worked answer

t = 3 s, so x = 36 m.

Key words

Distance: The total length of path travelled (scalar), in m.
Displacement: The distance in a stated direction from the start point (vector).
Speed: Distance travelled per unit time (scalar).
Velocity: The rate of change of displacement (vector).
Acceleration: The rate of change of velocity, in m/s².
Deceleration (retardation): Negative acceleration, meaning slowing down.
Uniform acceleration: Velocity changes by equal amounts in equal times.
Free fall: Motion under gravity alone.
g: Acceleration due to gravity, about 9.8 m/s² (take 10 m/s² unless told otherwise).
Scalar: A quantity with magnitude only.
Vector: A quantity with magnitude and direction.
Projectile: An object thrown into the air that then moves under gravity alone.

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