Description of Motion (Grade 10 NSC Matric Physical Sciences): Revision Notes

Description of Motion

Motion can be described in three different ways to help us understand how objects move. These methods give us different but related information about the same motion.

Three methods for describing motion

1. Words - Using descriptive language to explain movement
2. Diagrams - Visual representations showing position changes
3. Graphs - Mathematical plots showing relationships between quantities

We will examine three fundamental types of motion:

• Stationary object - when the object is not moving
• Uniform motion - when the object moves at constant velocity
• Motion at constant acceleration - when the object's velocity changes at a constant rate

Key definition: instantaneous speed

Instantaneous speed is the magnitude of instantaneous velocity. This means it has the same numerical value as velocity but no direction.

• Quantity: Instantaneous speed (v)
• Unit: metres per second (m·s⁻¹)

Stationary object

A stationary object does not move, so its position does not change over time. This is the simplest type of motion to understand.

Characteristics of a stationary object

• Position remains constant
• Displacement is zero (since position doesn't change)
• Velocity is zero (since displacement is zero)
• Acceleration is zero (since velocity is not changing)

The graphs above show the motion characteristics for a stationary object. Notice that:

• Position vs time: Horizontal line showing constant position
• Velocity vs time: Horizontal line at zero
• Acceleration vs time: Horizontal line at zero

Understanding gradients in motion graphs

Gradient is a key concept for understanding motion graphs. From mathematics, we know:

Gradient (m) = change in y-value ÷ change in x-value = $\frac{\Delta y}{\Delta x}$

For a stationary object, all gradients are zero because nothing is changing.

Motion at constant velocity (uniform motion)

Uniform motion means the position of an object changes at the same rate over time. The object moves with constant velocity.

This diagram shows uniform motion - equal distances covered in equal time intervals.

Characteristics of uniform motion

• Position increases (or decreases) linearly with time
• Velocity remains constant (not changing)
• Acceleration is zero (since velocity is constant)

The graphs show distinctive patterns for uniform motion:

• Position vs time: Straight diagonal line (linear relationship)
• Velocity vs time: Horizontal line showing constant velocity
• Acceleration vs time: Horizontal line at zero

Calculating velocity from position graphs

For uniform motion, we can calculate velocity using the fundamental kinematic equation:

$v = \frac{\Delta x}{\Delta t} = \frac{x_f - x_i}{t_f - t_i}$

Where:

• $v$ = velocity
• $\Delta x$ = change in position
• $\Delta t$ = change in time
• $x_f$ = final position, $x_i$ = initial position
• $t_f$ = final time, $t_i$ = initial time

Motion with negative velocity

Objects can also move with constant velocity in the negative direction.

These graphs show motion with constant negative velocity:

• Position decreases linearly (downward sloping line)
• Velocity is constant but negative
• Acceleration remains zero

Motion at constant acceleration

The final type of motion occurs when an object has constant acceleration. This means the velocity changes at a constant rate.

Understanding constant acceleration

When acceleration is constant, several important patterns emerge:

• Velocity changes by the same amount in each equal time interval
• Position changes follow a curved (parabolic) pattern
• Acceleration remains constant (horizontal line on acceleration graph)

This diagram shows a bus accelerating from rest. Notice how the distances covered increase: 2.5 m, then 10 m, then 22.5 m, then 40 m in equal time intervals.

Calculating velocities during acceleration

To find velocity at different times, we calculate the gradient of position vs time at those points:

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

Calculating acceleration

The fundamental equation for acceleration is:

$a = \frac{\Delta v}{\Delta t}$

For constant acceleration: $a = \frac{v_f - v_i}{t_f - t_i}$

Using our bus example: $a = \frac{17.5 - 7.5}{4 - 2} = \frac{10}{2} = 5 { m·s}^{-2}$

These graphs show motion with constant acceleration starting from rest:

• Position: Curved (parabolic) line
• Velocity: Straight diagonal line
• Acceleration: Horizontal line showing constant acceleration

Summary of motion graphs

This comprehensive comparison shows the distinctive graph shapes for all three types of motion:

Using area under graphs

For velocity vs time graphs, the area under the curve equals displacement:

• Rectangle area = length × width = velocity × time = displacement
• Triangle area = ½ × base × height = ½ × time × velocity change
• Total displacement = sum of all areas (considering positive/negative directions)

Practical investigation: motion at constant velocity

Aim

To measure position and time during motion at constant velocity and determine average velocity from a "Position vs Time" graph.

Method

The experimental procedure involves systematic measurement and analysis:

1. Time a battery-operated toy car as it travels different distances
2. Record measurements in a data table
3. Repeat measurements and calculate averages
4. Plot a "Distance vs Time" graph
5. Find the gradient - this gives the average velocity

Distance (m)	Time (s)
	1	2	Ave.
0
0.5
1.0
1.5
2.0
2.5
3.0

Key observations

• Constant velocity produces a straight line graph
• Steeper gradient = faster velocity
• Gradient = rise/run = distance/time = velocity

Worked example: interpreting position-time graphs

Exam tips for motion graphs

Remember!

The three types of motion have distinct characteristics:

• Stationary objects have zero velocity and acceleration
• Uniform motion has constant velocity and zero acceleration
• Constant acceleration produces curved position graphs and linear velocity graphs

Master these patterns and you'll excel at interpreting any motion graph!