Distance, Displacement, Speed and Velocity

Ever wonder why physics needs special terms to describe movement? It's all about being precise. In physics, we distinguish between scalar quantities (which have only size) and vector quantities (which have both size and direction).

Distance is a scalar quantity measuring the total path length an object travels, measured in metres (m). Think of it as the actual ground covered. When you walk to school taking a winding route, your distance is the total length you walked.

Displacement is a vector quantity measuring the straight-line distance from start to finish in a specific direction, also measured in metres (m). If you drew an arrow from your starting point to your ending point, that's displacement.

Remember this! Distance tells you how far you've travelled, while displacement tells you how far you are from where you started. They use the same unit (metres) but represent different concepts.

Scalar vs Vector Quantities

When describing movement, we need to be precise about whether direction matters. This is where the difference between speed and velocity becomes crucial.

Speed is a scalar quantity measuring how fast something moves, calculated as distance ÷ time and measured in metres per second $m/s$. It tells you the rate of distance change but says nothing about direction.

Velocity is a vector quantity measuring how fast something moves in a specific direction, calculated as displacement ÷ time and measured in metres per second $m/s$. It tells you the rate of displacement change.

Consider walking to the shop: if you walk 300m down one road, then turn and walk 400m along another, your total distance is 700m. However, your displacement is only 500m (calculated using Pythagoras' theorem) in a specific direction.

Top tip: If you walk from home to the shop and back again, your total distance might be 1400m, but your final displacement is zero! This is a classic exam question that catches many students out.

Calculating Speed and Velocity

The formulas for speed and velocity look similar but use different quantities:

Average Speed = Total Distance ÷ Time Taken → v = d/t

Average Velocity = Displacement ÷ Time Taken → v = s/t

When an object moves in a straight line, the magnitude of displacement equals the distance, making the magnitude of velocity equal to speed. However, when direction changes, these values differ.

Remember these unit conversions:

• To convert km/h to m/s: divide by 3.6
• To convert m/s to km/h: multiply by 3.6

A key difference between these quantities appears in circular motion. If you complete one lap around a track, you've covered a significant distance, but your displacement is zero (you're back where you started). This means your average speed is positive, but your average velocity is zero!

Exam alert: Questions often ask about round trips. Remember that when you return to your starting point, displacement is zero, making average velocity zero regardless of the distance travelled.

Worked Examples

Let's apply these concepts with two examples:

Example 1: Straight-Line Motion A car travels 120 km on a straight motorway in 1.5 hours. Since the motion is in a straight line, the magnitude of displacement equals distance (120 km).

Average Speed = 120 km ÷ 1.5 h = 80 km/h Average Velocity = 80 km/h in the direction of travel

Example 2: Motion with Direction Change A student walks 80m North, then 60m East, taking 100 seconds.

Total distance = 80m + 60m = 140m Displacement magnitude (using Pythagoras) = √(80² + 60²) = 100m Average Speed = 140m ÷ 100s = 1.4 m/s Average Velocity magnitude = 100m ÷ 100s = 1.0 m/s

This clearly shows how speed and velocity can differ when direction changes.

Pro tip: Always specify direction for vectors. Velocity can be positive or negative to indicate direction $+10 m/s for right, -10 m/s for left$, while speed is always positive.

Key Points to Remember

You've now mastered the fundamental concepts of motion! Here's what you need to remember:

Scalar vs Vector: Scalars have magnitude only; vectors have magnitude and direction. Distance and speed are scalars; displacement and velocity are vectors.

Direction matters: For vectors, direction is essential. Always include direction when calculating velocity or displacement.

Displacement vs Distance: Displacement can never exceed distance. They're equal only in straight-line motion.

Round trips: If you end where you started, displacement is zero, making average velocity zero regardless of distance travelled.

When approaching exam questions, watch for scenarios involving changes in direction or round trips. These are designed to test your understanding of the scalar/vector distinction.

Exam success strategy: Questions often involve situations where speed and velocity have different values. If you're asked for velocity but calculate speed (or vice versa), you'll lose marks. Always check whether the question is asking for a scalar or vector quantity.