Distance-Time Graph: Formula, Importance & Plotting

Distance-time graph, in a given time period, helps to show how far an object has travelled. It can be expressed as a simple line graph which represents the distance versus time findings on the graph.

• Distance, in this case, is plotted on the Y-axis
• Time, in this case, is plotted on the X-axis

It is important when studying the motion of bodies. A distance-time graph can be obtained if the distance and time for the motion of a body are plotted on a rectangular graph, thus corresponding to the motion of that body.

• In case it is a straight line, then the motion is uniform.
• In case it has been provided, its speed can be estimated by means graph’s slope.
• The slope of the straight-line graph is the same, despite the chosen interval.
• It indicates that the speed of an object under uniform motion is constant.

Key Terms: Distance, Time, Motion, Speed, Uniform Motion, X-Axis, Y-Axis, Uniform Speed, Time Interval, Velocity, Distance-Time Graph

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Distance-Time Graph

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A Distance-Time graph can be defined as:

• ‘Distance’ is the total length that is travelled by an object.
• ‘Time’ can be defined by the minutes, hours, or seconds needed to cover this distance by the object. 

Distance-Time Graph

When these units of Distance and Time are placed on the X and Y axes of a graph to define the Distance covered and the time used by the object to do so, it is called a Distance-Time graph.

• On the X-axis, the time is plotted.
• On the Y-axis, the distance is plotted.

Note: The Curved lines on a distance-time graph denote that the speed is changing.

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Example of Distance-Time Graph

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To Distance-Time graph example can be shown via uniform motion.

• Suppose a driver drives at a constant speed shown by the speedometer.
• The driver measures the time taken by the bus for each kilometre. The driver finds out that the bus travels 1 kilometre for every 2 minutes.
• Thus, he creates a graph to represent the same. By this table, the speed he found is: ½ × 60 = 30 km/hr.
• The graph has been found to be in a straight line, while the motion of the bus is uniform.
• As per the graph, the speed of the bus at any instant time can be determined.

Data Table of Distance-Time Graph

The initial and final position of the car is:

= \(Speed = \frac{(Final Position-Initial position)}{Time}\)

The slope of the line can also be determined by a rectangle drawn anywhere near the straight line, helping to find the speed of the bus. In case an object is not moving, the distance-time graph can be found in a horizontal line, showing that the object is at rest.

Thus,

Distance-Time Graph

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Plotting Distance-Time Graph

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In a Distance-Time graph, the values of distance and time are plotted on the Y-axis and X-axis respectively. 

Note: Curved lines on a Distance-Time graph represent a change in the speed of the object, while a straight line indicates constant speed throughout the distance covered by the object.

• The Distance-Time graph is a linear graph where a line graph is plotted to denote the distance versus time values of an object on the graph.
• To do this, we have to first take a graph sheet and draw two perpendicular lines, naming them the X-axis horizontally and the Y-axis vertically.
• The X-axis shall indicate the distance travelled by the object and the Y-axis indicates the time required to cover this distance.
• Distance-Time graph for uniform motion is a straight line.

Read More: Average Acceleration Formula

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Distance-Time Graph Formula

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The values of a Distance-Time graph can be easily calculated from the slope or gradient on the linear graph. The gradient of the line drawn on a distance-time graph is equal to a moving object’s speed.

The gradient is directly proportional to the speed of the object, that is, the greater the gradient or steeper the line, the faster is the speed of the moving object. Thus, the formula of Distance-Time Graph is:

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Importance of Distance-Time Graph

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There are a number of applications of Distance-Time graphs. Some include:

• They provide great observation to study the motion of an object and determine the change in the position of an entity.
• The incline on this graph denotes the speed of the object.
• If an object’s distance and time of motion are recorded and plotted on a rectangular graph, a distance-time graph shall be constructed that corresponds to the motion of the body.

Distance vs. Time Definition

In the distance-time graph study, the three important components noted were:

• Time
• Speed
• Distance

The vertical Y-axis of the plotted graphical representation can be denoted as the vertical time axis. The horizontal X-axis can be defined as the horizontal distance axis. After the axes are determined, the values can easily be plotted on the graph.

Read More: Path Length

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Things to Remember

• A Distance-Time graph is a graph that represents how far an object has travelled in a given time.
• In a Distance-Time graph, the values of distance and time are plotted on the Y-axis and X-axis respectively.
• The values of speed of an object can be easily calculated from the slope or gradient of a Distance-Time graph.
• These graphs provide great observation to study the motion of an object and determine the change in the position of an entity.
• If the line on a Distance-Time graph is uniform, then the speed of the object is constant.

Also Read:

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Important Notes PDF on Motion

Notes on the chapter motion are given below:

Important Notes on Motion