IB MYP 4-5 Physics- Motion graphs- Study Notes - New Syllabus
IB MYP 4-5 Physics- Motion graphs- Study Notes
Key Concepts
- Position–Time Graph (Displacement–Time Graph)
- Velocity–Time Graph
- Acceleration–Time Graph
Position–Time Graph (Displacement–Time Graph)
Position–Time Graph (Displacement–Time Graph)
This graph shows how the position (or displacement) of an object changes with time. Time is plotted on the x-axis and position/displacement on the y-axis.
Key Features:
- Gradient = Velocity: A steeper gradient means a higher speed.
- Positive Slope: Motion in the forward direction (positive velocity).
- Negative Slope: Motion in the reverse direction (negative velocity).
- Zero Slope (Flat line): Object is stationary.
- Curved Line: Changing velocity → Acceleration is present.
Typical Shapes and Their Meaning:
| Graph Shape | Interpretation |
|---|---|
| Straight line with positive slope | Constant velocity (uniform motion) |
| Flat horizontal line | Object is stationary |
| Straight line with negative slope | Moving in opposite direction at constant speed |
| Curved upward line | Object is accelerating |
| Curved downward line | Object is decelerating |
Example:
An object moves such that its displacement-time graph is a straight line sloping upwards. What can you say about its motion?
▶️ Answer/Explanation
Since the displacement increases uniformly over time, the object is moving at constant velocity.
The graph’s straight-line nature and constant slope confirm there is no acceleration.
Final Answer: \( \boxed{\text{Constant velocity motion}} \)
Velocity–Time Graph
Velocity–Time Graph
This graph shows how an object’s velocity changes with time. Time is plotted on the x-axis and velocity on the y-axis.
Key Features:
- Gradient = Acceleration: A steeper slope means greater acceleration.
- Positive Gradient: Object is accelerating.
- Negative Gradient: Object is decelerating (slowing down).
- Zero Gradient (flat line): Constant velocity.
- Area under the graph = Displacement
Typical Shapes and Their Meaning:
| Graph Shape | Interpretation |
|---|---|
| Horizontal line above time axis | Constant positive velocity |
| Line sloping upwards from zero | Uniform acceleration |
| Line sloping downwards to zero | Uniform deceleration |
| Line below time axis | Negative velocity (moving in opposite direction) |
Example:
An object accelerates uniformly from rest to a velocity of \( 20\,\text{m/s} \) in 4 seconds. Calculate its acceleration and the displacement covered in this time.
▶️ Answer/Explanation
Step 1: Find acceleration
Using the formula: \( a = \dfrac{v – u}{t} \)
\( a = \dfrac{20 – 0}{4} = \dfrac{20}{4} = 5\,\text{m/s}^2 \)
Step 2: Find displacement using area under graph
This is a triangle: \( \text{Area} = \dfrac{1}{2} \times \text{base} \times \text{height} \)
\( s = \dfrac{1}{2} \times 4 \times 20 = 40\,\text{m} \)
Final Answers:
- Acceleration = \( \boxed{5\,\text{m/s}^2} \)
- Displacement = \( \boxed{40\,\text{m}} \)
Acceleration–Time Graph
Acceleration–Time Graph
This graph shows how the acceleration of an object changes over time. Time is on the x-axis and acceleration is on the y-axis.
Key Features:
- Horizontal Line Above Time Axis: Constant positive acceleration.
- Horizontal Line on Time Axis: Zero acceleration (uniform motion).
- Horizontal Line Below Time Axis: Constant negative acceleration (deceleration).
- Area Under the Graph = Change in Velocity
Typical Shapes and Their Meaning:
| Graph Shape | Interpretation |
|---|---|
| Horizontal line above x-axis | Constant acceleration |
| Horizontal line below x-axis | Constant deceleration |
| Line on x-axis | No acceleration (zero, steady velocity) |
Example:
An acceleration-time graph shows a constant value of \( 2\,\text{m/s}^2 \) over 5 seconds. Find the total change in velocity over this time.
▶️ Answer/Explanation
Step 1: Use area under the graph (rectangle):
\( \Delta v = a \times t = 2 \times 5 = 10\,\text{m/s} \)
Final Answer: \( \boxed{10\,\text{m/s}} \)