Can speed be negative in IB Physics?

No, speed cannot be negative because it is the magnitude of velocity. A speed may be positive or zero, but a negative value would not be physically meaningful under the standard definition. Velocity can have a negative component because its sign represents direction relative to a chosen axis. For example, if east is positive, a velocity of $-12\ \text{m s}^{-1}$ means motion west at a speed of $12\ \text{m s}^{-1}$. If a calculation produces negative speed, check whether you have actually calculated velocity or need to take the magnitude.

Can an object have constant speed but changing velocity?

Yes, an object can maintain constant speed while its velocity changes because velocity includes direction. A car moving uniformly around a circular track is the standard example: its speed remains constant, but the direction of motion changes continuously. Its instantaneous velocity is tangent to the circular path at each point. Because velocity is changing, the car has acceleration directed toward the centre of the circle. Constant velocity would require both constant speed and an unchanging direction.

When are average speed and average velocity equal?

Average speed equals the magnitude of average velocity when an object moves along a straight line without reversing direction during the chosen interval. Under those conditions, total distance equals the magnitude of displacement. The velocity must still include a direction, while speed does not. If the object turns, reverses, or follows a curved path, distance will generally exceed the magnitude of displacement. Average speed will then be greater than the magnitude of average velocity.

Why is average velocity zero after a complete lap?

After a complete lap, the object returns to its initial position, so its displacement for the full interval is zero. Average velocity is displacement divided by elapsed time, giving a value of zero. The distance travelled is not zero because the object has covered the entire circumference of the track. Its average speed is therefore positive as long as it completed the lap in a finite time. The zero average velocity describes the net change in position, not the object's motion at every instant.

What is the difference between instantaneous speed and average speed?

Instantaneous speed describes how fast an object is moving at one particular moment. Average speed is the total distance travelled divided by the total elapsed time over an interval. A speedometer approximately shows instantaneous speed, while a journey calculation using total distance and time gives average speed. The two values are equal throughout an interval only if speed remains constant. Instantaneous speed is also the magnitude of instantaneous velocity, whereas average speed is not generally the magnitude of average velocity.

How do I find speed and velocity from a velocity-time graph?

The graph's vertical coordinate gives instantaneous velocity, including its sign, at each time. Instantaneous speed is the magnitude of that coordinate, so a velocity of $-5\ \text{m s}^{-1}$ corresponds to a speed of $5\ \text{m s}^{-1}$. The signed area between the graph and time axis gives displacement, with regions below the axis counted as negative. Adding the absolute values of all areas gives total distance travelled. Divide displacement by elapsed time for average velocity, or divide total distance by elapsed time for average speed.

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What is the difference between speed and velocity?

• 29 Jul 2026•16

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What is the difference between speed and velocity?

• 29 Jul 2026•16

Speed and velocity both describe how an object's position changes over time, but they are not interchangeable. Speed is a scalar quantity that tells you how fast an object moves, while velocity is a vector quantity that tells you both how fast it moves and in which direction.

The distinction depends on an equally important pair of ideas: speed is associated with distance, whereas average velocity is calculated from displacement. This single difference affects calculations, graph interpretation, circular motion, acceleration, and the wording of IB Physics answers.

In the current IB Physics course, these ideas belong to A.1 Kinematics within the theme Space, time and motion. The distinction is required at both SL and HL, and it supports later work on acceleration, projectiles, momentum, and circular motion. For broader topic coverage, use IB Physics Kinematics Explained for Exams; this article concentrates specifically on speed vs velocity.

Speed vs velocity at a glance

Feature	Speed	Velocity
Type of quantity	Scalar	Vector
Information required	Magnitude only	Magnitude and direction
Average value	Total distance divided by elapsed time	Displacement divided by elapsed time
Instantaneous relationship	Magnitude of instantaneous velocity	Rate of change of position
Can it be negative?	No	A component can be negative relative to a chosen axis
SI unit	m s⁻¹	m s⁻¹
Everyday example	15 m s⁻¹	15 m s⁻¹ east

A scalar is fully described by a numerical magnitude and unit. A vector requires a magnitude, unit, and direction, although direction can also be represented by a sign when motion occurs along one axis.

Both quantities use the coherent SI derived unit metre per second, written m s⁻¹. The unit alone therefore does not reveal whether a value represents speed or velocity; you must examine the definition, direction, sign, and context.

What is speed in physics?

Speed is the magnitude of velocity. It describes how fast an object is moving without specifying where it is going. A car travelling at 20 m s⁻¹, for example, has the same speed whether it is moving north, south, or around a bend.

For motion over a finite time interval, average speed is defined as:

\text{average speed} = \frac{\text{total distance travelled}}{\text{elapsed time}}

Distance is the complete length of the path followed. It is a scalar and does not decrease because an object reverses direction. As a result, average speed is non-negative, provided elapsed time is positive.

Suppose a runner completes one 400 m lap in 80 s. The runner's average speed is:

\text{average speed} = \frac{400}{80} = 5.0\ \text{m s}^{-1}

This tells us the rate at which the runner covered path length. It says nothing about the runner's final direction or change in position.

Average speed and instantaneous speed

Average speed applies over an interval, such as an entire race or car journey. It does not mean that the object maintained that speed throughout the interval. A vehicle could stop, accelerate, and slow down while still having a well-defined average speed for the complete journey.

Instantaneous speed is the speed at one particular instant. A car's speedometer approximately displays instantaneous speed, not average speed. In one-dimensional motion, instantaneous speed is the absolute value of instantaneous velocity:

\text{instantaneous speed} = |v|

In more than one dimension, it is the magnitude of the velocity vector:

\text{speed} = |\vec{v}|

What is velocity in physics?

Velocity is the rate of change of position. Because a change in position is displacement, average velocity is calculated using:

\vec{v}_{\text{avg}} = \frac{\Delta \vec{x}}{\Delta t}

Here, $\Delta \vec{x}$ is displacement and $\Delta t$ is elapsed time. Displacement connects the initial position directly to the final position, including direction. It does not necessarily equal the path length travelled.

For example, a cyclist who moves 300 m east in 60 s has an average velocity of:

\vec{v}_{\text{avg}} = \frac{300\ \text{m east}}{60\ \text{s}} = 5.0\ \text{m s}^{-1}\text{ east}

Writing only 5.0 m s⁻¹ would give the magnitude but omit the direction required for a complete vector answer.

Instantaneous velocity

Instantaneous velocity is the velocity at a particular moment. Mathematically, it is the derivative of position with respect to time:

\vec{v} = \frac{d\vec{x}}{dt}

On a position-time graph, instantaneous velocity is the gradient of the tangent at the relevant point. A positive gradient represents velocity in the chosen positive direction, while a negative gradient represents velocity in the opposite direction.

Velocity must always be interpreted relative to a reference frame. A passenger may have zero velocity relative to a steadily moving train but a non-zero velocity relative to the ground. This is why a careful physics description identifies the object, reference frame, and positive direction.

Why distance and displacement create the difference

The clearest way to understand the difference between speed and velocity in physics is to compare distance with displacement.

Distance is the total path length travelled and is a scalar.
Displacement is the vector change from initial position to final position.
Average speed depends on total distance.
Average velocity depends on displacement.

Consider a student who walks 100 m east and then 60 m west in a total time of 40 s. The total distance is:

100 + 60 = 160\ \text{m}

The average speed is therefore:

\frac{160}{40} = 4.0\ \text{m s}^{-1}

Taking east as positive, the displacement is:

100 - 60 = 40\ \text{m east}

The average velocity is:

\frac{40}{40} = 1.0\ \text{m s}^{-1}\text{ east}

The same journey therefore produces an average speed of 4.0 m s⁻¹ and an average velocity of 1.0 m s⁻¹ east. The values differ because retracing part of the route increases distance but reduces displacement.

A complete round trip

A runner who completes a full lap finishes at the starting position. The total distance is the circumference of the track, but the displacement is zero. Consequently, the runner has a positive average speed but zero average velocity for the complete lap.

This does not mean the runner's velocity was zero throughout the lap. At every moving instant the runner had an instantaneous velocity tangent to the track, and that direction changed continuously. Only the displacement over the complete interval was zero.

When speed and velocity have the same magnitude

Average speed equals the magnitude of average velocity only under specific conditions. The object must travel along a straight line without reversing direction during the selected interval. In that case, distance equals the magnitude of displacement.

For example, a train travelling 600 m east along a straight track in 30 s has:

Average speed: $600/30 = 20\ \text{m s}^{-1}$
Average velocity: $20\ \text{m s}^{-1}$ east
Magnitude of average velocity:

If the train reverses, follows a curved route, or returns toward its starting point, total distance becomes greater than the magnitude of displacement. Therefore:

\text{average speed} \geq |\text{average velocity}|

Equality occurs only when the distance travelled equals the magnitude of displacement. Do not assume that average speed is always the magnitude of average velocity.

Direction, signs, and negative velocity

In one-dimensional IB Physics questions, direction is often represented by a sign. You first define a positive direction, such as east is positive or upward is positive. Motion in the opposite direction then has negative velocity.

A velocity of $-8.0\ \text{m s}^{-1}$ does not mean the object is moving slowly or has an impossible negative speed. It means the object moves at a speed of 8.0 m s⁻¹ in the negative direction.

Velocity	Speed	Interpretation if east is positive
$+6\ \text{m s}^{-1}$	$6\ \text{m s}^{-1}$	Moving east
$- 6 {m s}^{}$

A negative velocity also does not automatically mean that the object is slowing down. Speed decreases when velocity and acceleration point in opposite directions. If both velocity and acceleration are negative, the object speeds up while moving in the negative direction. This sign reasoning is developed further in how to find acceleration from velocity and time.

Constant speed does not always mean constant velocity

A moving object has constant velocity only if both its speed and direction remain constant. Constant speed alone is not sufficient.

A car travelling around a circular track at a steady 12 m s⁻¹ has constant speed, but its velocity changes because its direction changes continuously. Since acceleration is the rate of change of velocity, the car is accelerating even though its speed remains unchanged. In uniform circular motion, this acceleration points toward the centre of the circle.

This distinction matters well beyond basic IB Physics kinematics. Momentum is $\vec{p}=m\vec{v}$ , so momentum changes when velocity direction changes. Similarly, acceleration can result from a change in speed, direction, or both.

By contrast, an object moving at constant velocity follows a straight line at constant speed in a fixed direction. Its acceleration is zero.

How speed and velocity appear on graphs

Graph questions often test the distinction without asking for a written definition. Begin by reading both axes and their units.

Position-time graphs

The gradient of a position-time graph gives velocity:

v = \frac{\Delta x}{\Delta t}

A positive gradient means positive velocity.
A negative gradient means negative velocity.
A horizontal line means zero velocity.
A steeper gradient means a greater speed because speed is the magnitude of the gradient.
A changing gradient means the velocity is changing.

For a curved position-time graph, draw a tangent to determine instantaneous velocity. Use two well-separated points on the tangent rather than two points on the original curve.

Velocity-time graphs

A velocity-time graph can lie above or below the time axis because velocity is signed. The signed area between the graph and the time axis gives displacement, while the total absolute area gives distance travelled.

For example, an area of $+30$ m above the axis followed by an area of $-10$ m below it gives:

Displacement: $30 + (-10) = 20$ m
Distance: $30 + 10 = 40$ m

If the interval lasts 10 s, average velocity is $2.0$ m s⁻¹ in the positive direction, while average speed is $4.0$ m s⁻¹. The RevisionDojo A.1 Kinematics study notes provide broader treatment of motion graphs and equations.

A reliable IB exam method

When a question involves speed or velocity, use the following sequence:

Identify the requested quantity. Underline speed, velocity, distance, or displacement.
Define a positive direction. This is essential when velocities, displacements, or accelerations can be negative.
Choose the correct numerator. Use total distance for average speed and displacement for average velocity.
Use the complete elapsed time. Include stopping time unless the question explicitly excludes it.
State the direction of a vector. Give a compass direction, angle, or sign tied to your chosen axis.
Include an appropriate unit. In SI calculations, this will usually be m s⁻¹.
Check plausibility. Average speed cannot be less than the magnitude of average velocity for the same interval.

For multi-stage motion, make a short table listing each stage's distance, displacement, and time. This prevents a common error in which signed displacements are added when the question asks for total distance.

After reviewing the concept, practise mixed calculations in the A.1 Kinematics Questionbank. The A.1 Kinematics resource hub also connects notes, videos, flashcards, and exam-style practice.

Common speed vs velocity mistakes

Using the terms interchangeably

In everyday speech, people often use speed and velocity as synonyms. In an IB Physics response, however, writing that velocity is simply “how fast something moves” is incomplete because it omits direction.

A stronger definition is: velocity is the rate of change of position and is a vector quantity. For average velocity, explicitly refer to displacement divided by elapsed time.

Averaging the initial and final speeds automatically

The expression $(u+v)/2$ gives average velocity only when velocity changes linearly with time, as it does under constant acceleration in one dimension. It is not a universal definition of average speed or average velocity.

If a journey contains several stages, use total distance divided by total time for average speed. For average velocity, use overall displacement divided by total time.

Forgetting stationary time

If a cyclist travels for 20 s and rests for 10 s, the elapsed time for the complete journey is 30 s. Omitting the rest interval produces an incorrectly high average speed and average velocity.

Treating negative velocity as negative speed

Speed is the magnitude of velocity and is therefore non-negative. Convert a one-dimensional velocity to speed by taking its absolute value, but retain the sign when velocity itself is required.

Confusing a complete trip with one stage

The selected time interval controls the answer. A runner may have non-zero average velocity over half a lap but zero average velocity over a complete lap. Always mark the start and finish positions for the exact interval stated.

More diagnostic examples are available in IB Physics Kinematics: Common Mistakes and Fixes.

Conclusion

The essential difference is that speed is a scalar magnitude, while velocity is a vector with magnitude and direction. Average speed uses total distance, whereas average velocity uses displacement. Instantaneously, speed is the magnitude of velocity, but average speed is not generally the magnitude of average velocity.

For exams, define a positive direction, distinguish path length from change in position, interpret graph areas and gradients carefully, and include direction in vector answers. RevisionDojo's Kinematics Notes, Questionbank, Flashcards, and Jojo AI can help you practise these distinctions until the correct method becomes automatic.

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