Position Time Graph

The Position–Time (x–t) graph shows how the position (x) of an object changes with time (t). For a stationary object, the position does not change over time — it remains constant.

👉 This is the simplest type of motion graph and helps students understand the meaning of zero velocity.

2. Definition

A stationary object is one that does not change its position with respect to a chosen reference point over time.

Mathematically:

[ x(t) = x_0 ]

where

• [ x(t) ] → Position of the object at time [ t ]
• [ x_0 ] → Constant position of the stationary object

Key Features of the Graph

1. The graph is a straight line parallel to the time (t) axis.
2. The position remains constant at [ x = x_0 ] for all values of time.
3. The slope of the line is zero, which means the velocity is zero:

[ v = \dfrac{dx}{dt} = 0 ]

Graph Description

• X-axis: Time [ t ]
• Y-axis: Position [ x ]
• The horizontal straight line indicates that the position does not change over time.

SI Unit and Dimensional Formula

• Position [ x ]: SI Unit → meter (m), Dimensional Formula → [ [L] ]
• Time [ t ]: SI Unit → second (s), Dimensional Formula → [ [T] ]
• Velocity [ v ]: SI Unit → m/s, Dimensional Formula → [ [L T^{-1}] ]

Practice Questions (With Solutions)

Conceptual Questions

1. What is the slope of the position-time graph for a stationary object?
   Solution: Zero, because position is constant.
2. What does the horizontal line in the graph represent?
   Solution: The object’s position remains unchanged.

Numerical Questions

3. The position of an object is [ x = 5 , \text{m} ] for 10 seconds. Draw the position-time graph and find its velocity.
   Solution:Graph: A horizontal straight line at [ x = 5 , \text{m} ] from [ t = 0 ] to [ t = 10 , \text{s} ].

   Velocity:
   [ v = \dfrac{\Delta x}{\Delta t} = \dfrac{5 – 5}{10} = 0 , \text{m/s} ]

FAQs / Common Misconceptions

Q1: Does a horizontal line mean the object is at the origin?
❌ No. It means the position is constant. The line can be above or below the origin depending on the initial position.

Q2: If the line is parallel to the x-axis at [ x = 3 , \text{m} ], what does it mean?
✅ The object stays 3 m away from the reference point and does not move.

Q3: Can the graph for a stationary object be a vertical line?
❌ No. A vertical line would mean the object changes position at the same instant of time, which is not physically possible.adobe