Class 9 Physics Chapter 1: Motion – Displacement Time Ghraps Notes

Displacement-Time Graphs

1. Body at Rest

• Displacement remains constant over time.
• Velocity = 0, so the graph is a horizontal line.
• There is no motion and no acceleration.

2. Uniform Motion

• Displacement increases at a constant rate.
• Velocity is constant, so graph is a straight line with constant slope.
• Acceleration is zero.

5. Uniform motion (negetive velocity)

• Slope = negetive (angle > 90°)
• velocity is negetive
• Object returning towards starting point

Graph Line	Slope Sign	Velocity	Direction
Upward ↗	Positive	+	Moving away from origin
Horizontal →	Zero	0	Not moving (stationary)
Downward ↘	Negative	–	Returning towards starting point

4. Non-Uniform Motion

• 🔵 Blue curve: Constant positive acceleration — displacement increases rapidly.
• 🟢 Green curve: Constant negative acceleration — velocity decreases, motion slows down.
• 🔴 Red curve: Non-constant acceleration (acceleration increases with time) — displacement increases even more rapidly.

Quick Comparison Table

Shape of s–t Graph	Velocity	Acceleration	Interpretation
Straight line	Constant	Zero	Uniform motion
Smooth parabola	Changing	Constant	Uniform acceleration
Irregular curve	Changing	Changing	Non-uniform acceleration

5. Graph Not Possible

• line is parallel to displacement (Y-axis) or vertical line
• Displacement is changing but time is constant.
• Thus this graph is not possible.

6. Object Moving, Coming to Rest Then returning

•  🟢 Green line (OP) represents: object is moving away from the initial position.
  [Here, displacement (s) is positive and increasing and Slope = velocity is positive.]
•  🔵 Blue line (PQ) represents: object is at rest.
  [Here, displacement (s) is constant and Slope = velocity is zero.]
• 🟡 Yellow line (QR) represents: returning to initial position.
  [Here, displacement (s) is positive but decreasing and Slope = velocity is negetive.]
• Point (R) represents: Object is now at initial position. 
• 🔴 Red line (RS) represents: The object has crossed the origin and is now on the other side of the reference point.
  [Here, displacement (s) is negetive and Slope = velocity is also negetive.]

🔁 Real-Life Example:

Let’s say:

You start walking east (let take it positive direction).

At some point,You stopped there for few minutes, then you turn around and walk west (negative direction).

If you cross your starting point and keep going west, your displacement becomes negative.

All the graph for distance-time is as except distance can't be negetive.