CIE IGCSE Physics (0625) Motion Study Notes - New Syllabus
CIE IGCSE Physics (0625) Motion Study Notes
LEARNING OBJECTIVE
- Understanding the concepts of Motion
Key Concepts:
- Distance–Time & Speed–Time Graphs
- Acceleration Due to Free Fall
- Falling in a Uniform Gravitational Field
Distance–Time & Speed–Time Graphs
Distance–Time Graphs
A distance–time graph shows how far an object has travelled over time.
- Gradient (slope) = speed
- Horizontal line → object is at rest
- Straight sloped line → constant speed
- Curved line → changing speed (acceleration/deceleration)
Speed–Time Graphs
A speed–time graph shows how an object’s speed changes over time.
- Gradient (slope) = acceleration
- Area under the graph = distance travelled
- Horizontal line → constant speed
- Upward slope → acceleration
- Downward slope → deceleration
- Curved lines → changing acceleration
Interpretation from a Distance–Time Graph
| Graph Shape | Interpretation |
|---|---|
| Flat horizontal line | Object is at rest |
| Straight upward line | Moving with constant speed |
| Curve getting steeper | Accelerating |
| Curve getting flatter | Decelerating |
Interpretation from a Speed–Time Graph
| Graph Shape | Interpretation |
|---|---|
| Horizontal line | Constant speed |
| Straight upward slope | Constant acceleration |
| Straight downward slope | Constant deceleration |
| Curved slope | Changing acceleration |
| Line on time axis | Object is at rest (speed = 0) |
Acceleration Types from Speed–Time Graphs
| Graph Type | Line Shape | Acceleration |
|---|---|---|
| Speed–Time | Straight slope | Constant acceleration |
| Speed–Time | Curved slope | Changing acceleration |
Example:
A distance–time graph shows a flat line from 0 to 10 seconds at 15 m. What does this mean?
▶️ Answer/Explanation
The distance does not change over time. This means the object is not moving.
Conclusion: The object is at rest for 10 seconds.
Example:
A cyclist travels 100 m in 20 seconds in a straight line. Draw and describe the distance–time graph.
▶️ Answer/Explanation
Speed = \( \dfrac{100}{20} = 5~\text{m/s} \)
The graph will be a straight diagonal line from (0, 0) to (20, 100).
Conclusion: The object moves with constant speed.
Example:
A car accelerates uniformly from 0 to 30 m/s in 6 seconds. Calculate the acceleration and distance travelled.
▶️ Answer/Explanation
Step 1: Acceleration
\( a = \dfrac{\Delta v}{\Delta t} = \dfrac{30 – 0}{6} = \boxed{5~\text{m/s}^2} \)
Step 2: Distance travelled (Area under triangle)
Area = \( \dfrac{1}{2} \times \text{base} \times \text{height} = \dfrac{1}{2} \times 6 \times 30 = \boxed{90~\text{m}} \)
Example:
The speed-time graph below shows the motion of a vehicle over a period of 30 seconds.
Use the graph to calculate the total distance travelled by the vehicle in 30 seconds.
Break the graph into the following intervals and calculate the distance for each:
- From 0 to 10 seconds (acceleration)
- From 10 to 25 seconds (constant speed)
- From 25 to 30 seconds (deceleration)
▶️ Answer/Explanation
From 0 s to 10 s (acceleration):
This is a triangle:
Distance = \( \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 10 \times 20 = \boxed{100~\text{m}} \)
From 10 s to 25 s (constant speed):
This is a rectangle:
Distance = \( \text{width} \times \text{height} = 15 \times 20 = \boxed{300~\text{m}} \)
From 25 s to 30 s (deceleration):
This is another triangle:
Distance = \( \frac{1}{2} \times 5 \times 20 = \boxed{50~\text{m}} \)
Total Distance Travelled:
\( 100 + 300 + 50 = \boxed{450~\text{m}} \)
Acceleration Due to Free Fall
Free Fall:
Free fall is the motion of an object under the influence of gravity alone.
- There is no air resistance involved during true free fall.
- The only force acting on the object is its weight (gravitational force).
Acceleration due to gravity (g):
- The acceleration an object experiences during free fall is due to Earth’s gravity.
- This acceleration is denoted by the symbol g.
- Its value is nearly constant near the surface of the Earth.
Standard value: \( g = 9.8~\text{m/s}^2 \)
Key points:
- This acceleration acts vertically downward.
- It does not depend on the mass of the object.
- All objects fall at the same rate in a vacuum, regardless of their weight or size.
- The value of \( g \) is approximately constant at Earth’s surface, but may vary slightly by location (altitude, equator vs poles).
Important Concept: The value of \( g \) is also the gravitational field strength, which means the force per unit mass acting on an object:
\( g = \dfrac{F}{m} \)
- Where \( F \) is the weight in newtons and \( m \) is mass in kilograms.
Units of acceleration:
- SI Unit of acceleration: $m/s^2$ (metres per second squared)
- This means the velocity of a free-falling object increases by 9.8 m/s every second.
Example:
A stone is dropped from a tower. What is its acceleration during free fall?
▶️ Answer/Explanation
Since no other force except gravity acts on the stone, it undergoes free fall.
Acceleration = \( \boxed{9.8~\text{m/s}^2} \), vertically downward.
Example:
If a ball falls freely from rest, what is its speed after 3 seconds?
▶️ Answer/Explanation
Use the equation: \( v = g \cdot t \)
Given: \( g = 9.8~\text{m/s}^2 \), \( t = 3~\text{s} \)
Then, \( v = 9.8 \times 3 = \boxed{29.4~\text{m/s}} \)
Falling in a Uniform Gravitational Field
Falling in a Uniform Gravitational Field
- In a uniform gravitational field (like near Earth’s surface), all objects experience the same downward acceleration due to gravity: \( g = 9.8~\text{m/s}^2 \).
- This gravitational pull acts on all objects equally regardless of their mass (ignoring air resistance).
Case 1: Falling Without Air or Liquid Resistance (Vacuum):
- No resistive force is acting — only gravity.
- All objects fall with the same acceleration: \( g = 9.8~\text{m/s}^2 \).
- Speed increases uniformly (i.e. object accelerates constantly).
Case 2: Falling With Air or Liquid Resistance:
- As the object falls, air or fluid pushes against it — this is a resistive force (also called drag).
- This resistance increases with speed.
- Eventually, the upward resistive force becomes equal to the object’s weight.
- At this point, net force = 0 and acceleration = 0.
This constant maximum speed is called: Terminal velocity
- The object continues falling at constant speed from this point onward.
Key forces involved:
- Weight (W) — acts downward and stays constant
- Air resistance (R) — acts upward and increases with speed
| Stage | Forces | Motion |
|---|---|---|
| Start of fall | Weight > Air resistance | Accelerates downward |
| Falling faster | Weight ≈ Air resistance | Acceleration decreases |
| Terminal velocity | Weight = Air resistance | Constant speed (no acceleration) |
Example:
A metal ball and a paper sheet are dropped in a vacuum. Which hits the ground first?
▶️ Answer/Explanation
There is no air resistance in a vacuum. Both objects fall with the same acceleration.
They hit the ground at the same time.
Example:
A skydiver jumps from a plane and eventually reaches a constant speed. What is happening?
▶️ Answer/Explanation
At first, the skydiver accelerates as weight > air resistance.
As speed increases, air resistance increases until it equals the weight.
No net force → No acceleration → Skydiver falls at terminal velocity.