Understanding the Slope of a Graph

📊 Slope of a Graph – Class 9 Physics

🔹 What is a Slope?

The slope of a graph represents the rate of change of one physical quantity with respect to another. It helps us understand how fast or slow one quantity changes compared to another.

Formula:
Slope = (Change in Y) / (Change in X) = (Y₂ - Y₁) / (X₂ - X₁)

🔹 Example 1: Speed from Distance-Time Graph

In a distance-time graph:

• X-axis = Time (s)
• Y-axis = Distance (m)

Example:
A body moves from (0 s, 0 m) to (4 s, 20 m).
Slope = (20 - 0) / (4 - 0) = 20 / 4 = 5 m/s
So, speed = 5 m/s.

🔹 Example 2: Simple Pendulum – T² vs L Graph

In the simple pendulum experiment, we measure the time period (T) for different lengths (L) of the pendulum. The graph plotted is:

• X-axis = Length (L) in m
• Y-axis = Square of Time Period (T²) in s²

The slope of this graph gives a relation between T² and L.

Example:
Two points on the graph: (0.2 m, 0.8 s²) and (0.4 m, 1.6 s²)
Slope = (1.6 - 0.8) / (0.4 - 0.2) = 0.8 / 0.2 = 4 s²/m
This slope can be used to calculate the value of acceleration due to gravity (g).

🔹 Common Graphs and Their Slopes

Graph Type	Physical Quantity	Slope Unit
Distance-Time	Speed	m/s
Velocity-Time	Acceleration	m/s²
T² vs L (Simple Pendulum)	Used to calculate g	s²/m

🔹 Why is Slope Important in Physics?

• It helps in determining physical quantities like speed, acceleration, and g.
• Gives insights into the relationship between two variables.
• Essential for analyzing experimental data.

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