"Types of motion" is searched about 1,200 times a month in the United States, mostly by Grade 6 to 8 students (and CBSE Class 6 and 7 students, where the chapter is literally called Motion and Measurement of Distances), and "positive acceleration" another 1,000 by Grade 7 to 9 students meeting their first motion graphs. This page gives the six types with examples and the overlaps, then acceleration: the definition, the formula, positive, negative and zero with worked examples, the direction-change case, the two graphs read properly, and uniform against non-uniform motion, with a printable sheet and practice. The equations for uniformly accelerated motion are on the SUVAT page; what causes acceleration is on the net force page.
Download the motion sheet with practice (PDF) (A4, the types chart and the acceleration rules with worked examples on page 1, the graphs and the practice set with answers on page 2, free).
What motion is
An object is in motion when its position changes with time, measured against something taken as fixed (the ground, the room, the Sun). Motion is relative: a passenger is at rest relative to the train and moving at 100 km/h relative to the platform. Rest is the absence of motion relative to the chosen reference.
The six types of motion
| Type | What moves how | Examples |
|---|---|---|
| Translational | the whole object moves from one position to another, every part by the same amount | a car on a road, a book pushed across a table, a lift, a thrown ball |
| Rectilinear (a kind of translational) | along a straight line | a train on straight track, a falling apple, a sprinter in the 100 m, a lift |
| Curvilinear (a kind of translational) | along a curved path | a thrown ball's arc, a car rounding a bend, a river's flow |
| Rotational | the object spins about an axis that may pass through it | a wheel, a spinning top, the Earth on its axis, a fan, a drill bit |
| Oscillatory (vibratory) | to and fro about a central rest position | a pendulum, a swing, a guitar string, a tuning fork, a piston |
| Periodic | repeats itself at equal intervals of time | the Earth's orbit (a year), a heartbeat, a clock's hand, the tides, every oscillation |
| Circular | along a circular path (a special curvilinear and periodic motion) | a satellite, a stone whirled on a string, the tip of a fan blade, a car on a roundabout |
| Random (irregular) | no fixed path or pattern | a bee in flight, smoke and dust particles (Brownian motion), a football in a match |
Lists differ between textbooks: some count rectilinear and curvilinear as two of the six; some add circular; some fold oscillatory into periodic. The exam wants you to name the type and justify it, so learn the definitions, not the count.
Combined motions. A rolling wheel translates (its centre moves forward) and rotates (it spins) at the same time. The Earth rotates (a day) and translates along its orbit (a year, also periodic and nearly circular). A sewing-machine needle oscillates while the wheel driving it rotates. A bowled cricket ball translates along a curve while spinning. Describing a real motion usually means naming two types.
What acceleration is
Acceleration is the rate of change of velocity:
a = (v − u) ÷ t, or a = Δv ÷ Δt
- u: initial velocity, v: final velocity, both in m/s
- t: time taken for the change, in s
- a: acceleration in m/s² (metres per second per second: how many m/s the velocity changes each second)
A car going from 0 to 24 m/s in 8 s accelerates at (24 − 0) ÷ 8 = 3 m/s²: every second it is moving 3 m/s faster. The acceleration of free fall near Earth's surface is 9.8 m/s²: a dropped object's speed grows by 9.8 m/s each second.
Velocity is a vector (speed with a direction), so velocity changes, and acceleration happens, in three ways: the speed increases, the speed decreases, or the direction changes.
Positive, negative and zero acceleration
Choose a positive direction first (usually the direction the object is moving at the start). Then:
| Velocity | Sign of (v − u) | Acceleration | Example | |
|---|---|---|---|---|
| Positive acceleration | increasing in the positive direction | positive | positive: speeding up | a car pulling away: 0 to 15 m/s in 5 s, a = +3 m/s² |
| Negative acceleration (deceleration, retardation) | decreasing in the positive direction | negative | negative: slowing down | braking: 20 m/s to 0 in 4 s, a = −5 m/s² |
| Zero acceleration | constant | zero | none: steady speed in a straight line | a train at 30 m/s on straight track |
The subtlety that separates Grade 9 from Grade 7: "negative acceleration" means acceleration pointing the negative way, which is slowing down only if the object is moving in the positive direction. A ball thrown upward (up positive) has a = −9.8 m/s² throughout: it slows on the way up and speeds up on the way down, with the same negative acceleration the whole time, and at the very top it has zero velocity and still −9.8 m/s² of acceleration.
Acceleration at constant speed. A car rounding a bend at a steady 50 km/h is accelerating, because its direction (and so its velocity) is changing. The acceleration points toward the centre of the curve (centripetal acceleration). Likewise a satellite in a circular orbit at constant speed accelerates continuously toward the Earth. "Constant speed means no acceleration" is true only in a straight line.
Six worked examples
- A cyclist speeds up from 4 m/s to 10 m/s in 3 s. a = (10 − 4) ÷ 3 = 2 m/s².
- A train slows from 40 m/s to 25 m/s in 30 s. a = (25 − 40) ÷ 30 = −0.5 m/s² (a deceleration of 0.5 m/s²).
- A stone dropped from a bridge. u = 0, a = 9.8 m/s². After 3 s, v = 0 + 9.8 × 3 = 29.4 m/s.
- A ball thrown up at 19.6 m/s (up positive). a = −9.8 m/s². Time to the top (v = 0): t = (0 − 19.6) ÷ (−9.8) = 2 s.
- A car travels at a constant 20 m/s for 10 s. a = (20 − 20) ÷ 10 = 0. Distance = 20 × 10 = 200 m.
- A sprinter reaches 11 m/s from rest in 2.5 s, then holds that speed. Acceleration in the first phase 4.4 m/s²; in the second phase 0.
The two graphs, read properly
Distance-time (or displacement-time) graph. Time along the bottom, distance up the side.
- Flat horizontal line: at rest.
- Straight sloping line: constant speed (uniform motion). Gradient = speed. Steeper means faster.
- Curve getting steeper: speeding up (accelerating). Curve flattening: slowing down.
- The graph never goes backwards in time and a distance-time graph never slopes down (displacement-time can, meaning returning).
Velocity-time graph. Time along the bottom, velocity up the side.
- Flat horizontal line above zero: constant velocity, zero acceleration.
- Straight line sloping up: constant positive acceleration. Gradient = acceleration.
- Straight line sloping down: constant negative acceleration (slowing if above the axis).
- Horizontal line on the axis: at rest.
- Area under the graph = distance travelled (a rectangle for constant velocity, a triangle for acceleration from rest, split into shapes otherwise).
The classic confusion: a sloping line on a distance-time graph is steady speed; a sloping line on a velocity-time graph is steady acceleration. Read the axis label before the shape.
Worked: a velocity-time graph rises from 0 to 12 m/s in 4 s, stays at 12 m/s for 6 s, then falls to 0 in 2 s. Accelerations: 3 m/s², 0, −6 m/s². Distance: triangle ½ × 4 × 12 = 24 m, rectangle 6 × 12 = 72 m, triangle ½ × 2 × 12 = 12 m; total 108 m.
Uniform against non-uniform motion
| Uniform motion | Non-uniform motion | |
|---|---|---|
| Definition | equal distances in equal intervals of time | unequal distances in equal intervals |
| Speed | constant | changing |
| Acceleration | zero | not zero |
| Distance-time graph | straight sloping line | curve |
| Example | a car on cruise control on a straight road; light in a vacuum | a bus in traffic; a falling stone; a ball rolling down a hill |
Uniformly accelerated motion is non-uniform motion with a constant acceleration (free fall without air resistance, a car accelerating steadily): the velocity-time graph is a straight sloping line and the SUVAT equations apply.
The mistakes that cost marks
- Treating speed and velocity as the same word. Velocity has direction; a change of direction is an acceleration.
- Saying negative acceleration always means slowing down. It means slowing only when the motion is in the positive direction.
- Saying zero velocity means zero acceleration (the top of a throw has v = 0 and a = −9.8 m/s²).
- Reading a sloping distance-time line as acceleration.
- Finding distance from a velocity-time graph by reading the velocity instead of the area.
- Writing m/s for acceleration. It is m/s².
- Calling the Earth's orbit "rotation". The Earth rotates on its axis and revolves around the Sun.
Where it sits in each curriculum
| Curriculum | When | What is expected |
|---|---|---|
| India (CBSE) | Class 6 (Motion and Measurement of Distances: the types of motion), Class 7 (Motion and Time: speed, distance-time graphs, oscillatory motion), Class 9 (Motion: velocity, acceleration, graphs, the equations) | the six types by name in Class 6 and 7; a = (v − u) ÷ t and graphs in Class 9 |
| US (NGSS) | MS-PS2-2 (Grades 6 to 8: forces and change of motion), HS-PS2-1 (motion graphs, acceleration) | types of motion in elementary and middle school, acceleration and graphs in Grade 8 or 9 physical science |
| England | KS3 (Year 7 or 8: speed, distance-time graphs, relative motion), GCSE Physics (velocity, acceleration, velocity-time graphs, gradient and area, uniform acceleration) | calculations and both graphs at GCSE |
| Australia | Year 7 (forces and motion), Year 10 (motion: speed, velocity, acceleration, graphs) | Year 10 for the formula and graphs |
| Canada (Ontario) | Grade 11 Physics SPH3U (kinematics: uniform and non-uniform motion, graphs) | graphs and uniform acceleration |
Practice (answers in the PDF)
- Name the type (or types) of motion of: a ceiling fan, a child on a swing, a car on a straight road, a rolling football, the Moon around the Earth.
- A motorbike accelerates from 5 m/s to 25 m/s in 8 s. Calculate its acceleration.
- A bus slows from 15 m/s to 3 m/s in 6 s. What is its acceleration, and what word describes it?
- A ball is thrown straight up at 14.7 m/s. How long does it take to reach the top, and what are its velocity and acceleration there?
- A velocity-time graph shows a horizontal line at 8 m/s for 5 s. What is the acceleration, and how far does the object travel?
- Explain why a car driving round a roundabout at a steady 20 km/h is accelerating.
Download the sheet and the practice set (PDF)
Where to get help
A 1-on-1 online physics class with a tutor who teaches CBSE Class 6 to 9, NGSS middle-school science, KS3 and GCSE physics and the Australian Years 7 to 10 every week: motion taught with a chosen positive direction written at the top of every problem and both graphs drawn by hand until the axis is read before the shape. The physics page lists the courses; the free 30-minute first class is a real lesson on this week's homework. Related pages: the five equations of motion, net force and Newton's laws of motion.
Questions parents ask
1What are the types of motion?
2What is acceleration?
3What is negative acceleration?
4Can an object have zero acceleration while moving?
5What is the difference between uniform and non-uniform motion?
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