Distance, Displacement, Speed and Velocity
In 2000, Cathy Freeman ran 400 m around the Sydney Olympic track but her displacement was 0 m — she finished exactly where she started.
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Q1 · If you walk 400 metres around an oval track and finish where you started, have you travelled any distance? Have you been displaced?
Q2 · A plane flies from Sydney to Melbourne at 800 km/h, then returns at the same speed. Is its velocity the same on both trips? Explain.
● Know
- Distance is a scalar quantity; displacement is a vector quantity with direction.
- Speed is a scalar quantity; velocity is a vector quantity with direction.
● Understand
- Scalar quantities have magnitude only; vector quantities have both magnitude and direction.
● Can do
- Calculate distance, displacement, speed, and velocity in simple scenarios.
Imagine two students walking to school: one takes a winding 1.2 km route along the streets, the other cuts across the oval for a straight 800 m path in a north-east direction. They cover different distances, but their displacement — the straight-line distance from start to finish with direction — might be the same if they live in the same place. This everyday observation reveals a fundamental split in physics: some quantities, like the 1.2 km walked, are scalars with only magnitude; others, like the 800 m north-east, are vectors with both magnitude and direction.
Distance is a scalar. If you walk 400 metres around an oval, your distance is 400 m, period. Displacement is a vector. After one complete lap, you are back where you started, so your displacement is zero. The direction matters for displacement but not for distance.
Speed is a scalar: 60 km/h tells you how fast but not which way. Velocity is a vector: 60 km/h north tells you both speed and direction. An object moving in a circle at constant speed is still changing velocity because its direction keeps changing.
A hiker walks 3 km east and then 4 km north. The total distance travelled is 7 km (scalar). But the displacement from start to finish is 5 km northeast (vector), calculated using Pythagoras theorem. The distance and displacement have different magnitudes and completely different meanings.
Australian Rules Football: AFL players run extraordinary distances during a match, often 15 km or more. But their displacement at the end of the game is close to zero because they return to the same bench. Coaches track both distance (for fitness) and displacement (for positional play).
Distance and displacement are just two words for the same thing. They are completely different concepts. Distance is path length; displacement is straight-line change in position. After a round trip, distance is large and displacement is zero. Treating them as synonyms leads to fundamental errors.
Sort each quantity as scalar or vector.
Displacement is defined as the straight-line distance from the starting point to the finishing point, together with the direction from start to finish. It is a vector. If you end up exactly where you started, your displacement is zero, regardless of how far you travelled.
This seems counterintuitive because you have clearly moved. But displacement does not describe your journey; it describes your net change in position. A courier who drives all day and returns to the depot has travelled a large distance but has zero displacement.
Displacement can be positive or negative depending on the chosen direction. If east is defined as positive, then moving 5 m east gives displacement +5 m, and moving 5 m west gives displacement -5 m. The sign carries directional information.
A swimmer dives to the bottom of a 2 m pool and returns to the surface. The distance travelled is 4 m (2 m down plus 2 m up). But the displacement is zero because the swimmer finishes at the same position. If we define upward as positive, the displacement during the descent is -2 m, and during the ascent is +2 m. The total displacement is -2 + 2 = 0 m.
Sydney to Hobart yacht race: Yachts sail over 600 nautical miles from Sydney to Hobart, but their displacement is simply the straight-line distance between the two cities, about 520 nautical miles southeast. Navigators use displacement for weather routing, while race records consider the actual distance sailed.
Displacement can never be larger than distance. Actually, displacement can equal distance but can never exceed it. In a straight-line journey with no change in direction, displacement and distance have the same magnitude. In any journey with turns, displacement is smaller than distance.
Speed and velocity are related but distinct. Speed is the rate at which distance is covered: speed = distance / time. Velocity is the rate at which displacement changes: velocity = displacement / time. Both are measured in metres per second, but velocity includes direction while speed does not.
This distinction has important consequences. An object moving in a circle at constant speed is constantly changing direction, which means its velocity is constantly changing. A car on a roundabout at 30 km/h has constant speed but changing velocity. Since acceleration is defined as change in velocity, the car is accelerating even though its speedometer reads steady.
Average speed and average velocity are calculated differently. Average speed uses total distance; average velocity uses total displacement. A runner who completes a 400 m lap in 60 seconds has average speed 400/60 = 6.67 m/s. But average velocity is zero because displacement is zero.
A plane flies from Melbourne to Perth at 800 km/h. Its speed is 800 km/h. Its velocity is 800 km/h west. On the return trip, its speed is still 800 km/h, but its velocity is 800 km/h east. The speed has not changed, but the velocity has reversed direction. This directional information is crucial for air traffic controllers.
Australian aviation navigation: Airservices Australia tracks aircraft using both speed and velocity. Speed tells them how quickly a plane is consuming fuel and covering distance. Velocity tells them where the plane will be in ten minutes, which is essential for maintaining safe separation between aircraft.
Constant speed means constant velocity. This is only true for straight-line motion with no direction changes. As soon as an object turns, its velocity changes even if its speed stays the same. This is one of the most important insights in mechanics and is the basis for understanding circular motion.
tells us how an object is moving. tells us how fast and in what .
Speed and velocity are often confused because they share the same units and are numerically equal in simple straight-line motion. But they are fundamentally different concepts. Speed is a scalar; velocity is a vector. Speed tells you how fast; velocity tells you how fast and in what direction.
Because velocity includes direction, it can be positive or negative. If you define north as positive, a car driving south at 60 km/h has velocity -60 km/h. Its speed is still 60 km/h (speed is always positive), but the negative sign on velocity tells you it is moving in the opposite direction.
Constant speed with changing direction is one of the most counter-intuitive ideas in physics. A satellite orbiting Earth at constant speed is accelerating because its velocity vector keeps changing direction. Your intuition says acceleration means speeding up or slowing down, but in physics, any change in velocity is acceleration.
A cricket ball is hit straight up at 20 m/s. On the way up, its velocity is +20 m/s (if up is positive). At the top, its velocity is momentarily zero. On the way down, its velocity is negative. But its speed is 20 m/s on the way up, zero at the top, and increasing on the way down. Velocity captures the directional reversal; speed only captures magnitude.
Australian V8 Supercars: Drivers at Mount Panorama circuit maintain high speeds through corners, but their velocity changes constantly because the track direction changes. The cars are accelerating even when the throttle is steady. Engineers analyse velocity vectors around the track to optimise racing lines.
Negative velocity means moving backwards. Negative velocity only means moving in the opposite direction to the chosen positive direction. If east is positive, west is negative. But west is not backwards; it is just a different direction. The sign convention is arbitrary and chosen for mathematical convenience.
Mastering the vocabulary of motion is essential. Each term has a precise definition. Distance is path length. Displacement is straight-line change in position. Speed is distance over time. Velocity is displacement over time. Scalar means magnitude only. Vector means magnitude plus direction.
When solving problems, identify whether the quantity asked for is a scalar or a vector. If the question asks for speed, you do not need to mention direction. If it asks for velocity, you must include direction. A velocity answer without direction is incomplete.
These definitions are not arbitrary; they reflect deep physical distinctions. Scalars add like ordinary numbers. Vectors add according to geometric rules. Walking 3 km east and 4 km north does not put you 7 km from your start; it puts you 5 km away. Vector addition is different from scalar addition.
A pilot flies 100 km east and then 100 km north. The distance travelled is 200 km. The displacement is about 141 km northeast. The average speed depends on total time; the average velocity is displacement divided by total time, directed northeast. Each quantity tells a different part of the story.
Australian Antarctic Division: Scientists traversing Antarctica use GPS to track both distance and displacement. Distance matters for fuel and supply calculations. Displacement matters for knowing their position relative to base camp. In featureless ice landscapes, confusing these two quantities could mean the difference between reaching a research station and running out of fuel.
Vectors are just complicated scalars. Vectors are not complicated scalars; they are a different kind of quantity with different mathematical rules. You cannot add velocities by simple addition if they are in different directions. Vector arithmetic requires either trigonometry or component breakdown.
- Distance
- Displacement
- Speed
- Velocity
- Scalar
- Vector
- Total length of path travelled
- Quantity with magnitude and direction
- Straight line from start to finish with direction
- Quantity with magnitude only
- Displacement per unit time with direction
- Distance travelled per unit time
Scalar and vector quantities appear everywhere in sport and daily life. A runner GPS watch displays distance (scalar). A football referee tracks player position (vector displacement from the ball). A speed gun measures speed (scalar). A weather report gives wind velocity (vector). Understanding which type of quantity you are dealing with helps interpret information correctly.
In team sports, coaches analyse player displacement to assess positioning. A soccer midfielder who runs 12 km but has small displacement may be working hard without contributing to attacking plays. A forward with large displacement toward the opponent goal is creating scoring opportunities. Distance tells you about work rate; displacement tells you about effectiveness.
The language of physics makes sports commentary more precise. Saying a player is fast is vague. Saying they have high speed but low velocity toward the goal tells a coach exactly what needs improvement. Physics terminology transforms subjective impressions into measurable, communicable quantities.
In a relay race, each runner covers 100 m (distance) but their displacement depends on the track shape. On a straight track, displacement equals distance: 100 m in the running direction. On a curved track, displacement is less than 100 m because the finish is not in the same direction as the start.
Australian Institute of Sport: The AIS in Canberra uses motion tracking systems that record both distance and displacement for athletes in training. Swimmers are analysed for distance per stroke (efficiency) and displacement down the pool (progress). Sprinters are tracked for velocity changes during acceleration phases.
In real life, nobody cares about displacement; distance is what matters. This depends on context. A delivery driver cares about distance because they are paid per kilometre. A rescue helicopter cares about displacement because it needs to reach a specific location. Both quantities matter; the important one depends on what problem you are solving.
You learned that distance and speed are scalars, while displacement and velocity are vectors that include direction.
A car drives 100 km north and then 100 km south in 4 hours. What is its average speed, and what is its average velocity?
The hook used a Sydney-to-Melbourne flight: 1426 km of total distance, but the plane returns to where it started — zero displacement. That contrast was meant to capture the difference between speed and velocity before you'd studied it.
Now that you understand distance, displacement, speed and velocity precisely, how would you explain to someone why a GPS app uses velocity (with direction) rather than just speed? Did the flight example make the distinction clearer than you expected?
1. Which of these is a vector quantity?
2. A person walks 3 m east and 4 m north. What is their displacement from the starting point?
3. A car travels at 60 km/h around a circular track at constant speed. Which statement is true?
4. What is the SI unit for speed?
5. An object returns to its starting position after moving. Its displacement is:
A student walks 400 m east, then 300 m north. Calculate the student's total distance travelled and their displacement from the starting point. Show your working. (3 marks)
Hint: Use Pythagoras' theorem for displacement.
Explain why the velocity of an object moving in a circle at constant speed is not constant. (3 marks)
Hint: Consider what happens to the direction of motion.
Describe the difference between distance and displacement, using a real-world example. (3 marks)
Hint: Think of a journey where the path is not a straight line.