Speed and Velocity Revision Notes for Grade 10 NSC Matric Physical Sciences

Speed and Velocity

What is average speed?

Average speed is the total distance travelled divided by the time taken for the journey. Speed tells us how fast an object is moving, regardless of which direction it travels.

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Definition: Average speed is the distance (D) travelled divided by the time (Δt) taken for the journey.

Quantity: average speed (vav)
Unit name: metre per second
Unit symbol: m·s⁻¹

The formula for average speed is:

$\text{average speed} = \frac{\text{distance}}{\text{time}}$

$v_{av} = \frac{D}{\Delta t}$

Speed is always a positive value because distance is always positive. Speed is also a scalar quantity, which means it only has magnitude (size) but no direction.

What is average velocity?

Average velocity is the change in position of an object divided by the time taken for that change to occur. Velocity tells us both how fast an object is moving and in which direction.

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Definition: Average velocity is the change in position of a body divided by the time it took for the displacement to occur.

Quantity: average velocity (v̄av)
Unit name: metre per second
Unit symbol: m·s⁻¹

The formula for average velocity is:

$\text{average velocity} = \frac{\text{change in position}}{\text{change in time}}$

$\bar{v}_{av} = \frac{\Delta \bar{x}}{\Delta t}$

Velocity can be positive or negative depending on the direction of motion. A positive velocity indicates movement in the positive direction you chose in your coordinate system, while a negative velocity indicates movement in the opposite direction. Velocity is a vector quantity, which means it has both magnitude and direction.

Key differences between speed and velocity

Understanding the differences between speed and velocity is crucial for solving motion problems correctly.

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Critical Differences Between Speed and Velocity:

Speed	Velocity
depends on the path taken	independent of path taken
always positive	can be positive or negative
is a scalar	is a vector
no dependence on direction and so is only positive	direction can be determined from the sign convention used (i.e. positive or negative)

Important note: When an object makes a round trip (travels away from its starting point and then returns to the same point), it has zero velocity but travels at a non-zero speed. This happens because the displacement is zero (it ends up where it started), but the total distance travelled is not zero.

Worked example: calculating speed and velocity

Let's work through a practical example to see how speed and velocity are calculated differently.

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Worked Example: Calculating Speed and Velocity

Problem: James walks 2 km away from home in 30 minutes. He then turns around and walks back home along the same path, also in 30 minutes. Calculate James' average speed and average velocity.

Solution:

Step 1: Identify what information is given and what is asked for

Distance out: 2 km in 30 minutes
Distance back: 2 km in 30 minutes
We need to find average speed and average velocity

Step 2: Check that all units are SI units The information is not in SI units, so we must convert:

1 km = 1 000 m
2 km = 2 000 m
1 min = 60 s
30 min = 1 800 s

Step 3: Determine displacement and distance

James started at home and returned home, so his displacement is 0 m: Δx̄ = 0 m
James walked a total distance of 4 000 m (2 000 m out and 2 000 m back): D = 4 000 m

Step 4: Determine total time

James took 1 800 s to walk out and 1 800 s to walk back
Total time: Δt = 3 600 s

Step 5: Calculate average speed $v_{av} = \frac{D}{\Delta t} = \frac{4\ 000\ \text{m}}{3\ 600\ \text{s}} = 1.11\ {m·s}^{-1}$

Step 6: Calculate average velocity $\bar{v}_{av} = \frac{\Delta \bar{x}}{\Delta t} = \frac{0\ \text{m}}{3\ 600\ \text{s}} = 0\ {m·s}^{-1}$

This example clearly shows why speed and velocity can be very different. James was moving the entire time (non-zero speed), but since he ended up where he started, his overall change in position was zero (zero velocity).

Understanding motion concepts

Average velocity tells us about the rate of change of position. It shows how much an object's position changes per unit of time. Since velocity is a vector, we use the symbol v̄av for average velocity to show it has direction.

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When solving problems, always remember to:

Use the correct formula (distance for speed, displacement for velocity)
Check your units and convert to SI units if necessary
Consider the sign of velocity based on your chosen coordinate system
Remember that speed is always positive, but velocity can be positive or negative

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Key Points to Remember:

Speed = distance ÷ time and is always positive (scalar quantity)
Velocity = displacement ÷ time and can be positive or negative (vector quantity)
Speed depends on the total path travelled, while velocity only depends on the starting and ending positions
An object returning to its starting point has zero velocity but non-zero speed
Always convert units to SI units (metres and seconds) before calculating

Speed and Velocity (Grade 10 NSC Matric Physical Sciences): Revision Notes