Distance Time Graph – GCSE Physics

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Introduction

  • Motion is the change in position of an object with respect to time.
  • The three fundamental quantities that describe Motion are:

Distance: It is the total path length covered by an object, regardless of direction.

Time: It is the duration over which Motion occurs.

Speed: It tells us how fast an object moves.

What is Speed and How is it Measure?

  • Speed is the measure of how fast an object moves.
  • It defined as the distance traveled per unit of time.
  • It is a Scalar Quantity.
  • Speed can be measured using the formula:

Common SI Units:

  • Meters per second (m/s)
  • Kilometers per hour (km/h)
  • Miles per hour (mph)

certified Physics and Maths tutorSolved Example

Problem: If a bike travels 150 meters in 10 seconds, what’s the speed of bike?

Solution: 

Step #1: Given

    • Distance: 150 m
    • Time Taken: 10s

Step #2: Using the formula:

Step #3: Putting the values and solve:

So, the speed of the bike is 15 meters per second (m/s)

Final Answer: 15 m/s

Speed, Distance and Time Triangle

  • The Speed, Distance and Time Triangle is an easy way to remember the relationship between speed, distance, and time.
  • It helps in calculating one quantity when the other two are known.

How to use Triangle:

  • To Find Speed: Cover “S” and the formula is,

  • To Find Distance: Cover “D” and the formula is,

  • To Find Time: Cover “T” and the formula is,

What is a Distance-Time Graph?

  • A Distance-Time Graph is a graphical representation of how distance changes over time.
  • It helps visualize the motion of an object.

Features of a Distance-Time Graph:

  • X-axis (Horizontal) → Represents Time (seconds, minutes, hours).
  • Y-axis (Vertical) → Represents Distance (meters, kilometers).
  • Slope of the Graph → Represents Speed.

Distance-Time graphs for various types of body motion:

  • In Distance-Time Graph, the Gradient of the line at any point tell us the Speed of the object is travelling.
  • Mathematically,

How to Calculate Speed from Distance-Time Graph?

Steps to Calculate Speed from the Graph:

  • Step#1: Observe the Graph.
  • Step#2: Identify Two Points on the Graph.
  • Step#3: Find the Change in Distance (Δd).
  • Step#4: Find the Change in Time (Δt).
  • Step#5: Calculate the Speed using formula,

Case 1: For Stationary body, it observed that the object is not moving. Since distance remains the same over time,

Case 2: For Uniform body, the graph is a straight line and the speed is constant.

Case 3: For Non-Uniform body, speed varies over time, so find instantaneous speed by calculating the slope of the tangent at a given point.

If Curved upwards → Acceleration (speed increasing).

If Curved downwards → Deceleration (speed decreasing).

certified Physics and Maths tutorSolved Example

Problem: The distance-time graph of an object shows a slope at 20 meters for 4 seconds. What is the speed of the object?

Solution: 

Step #1: Observe the Graph,

    • The Body is in Uniform Motion.

Step #2: Identify Two Points on the Graph:

    • At t1 = 0s, d1 = 0m.
    • At t2 = 4s, d2 = 20m.

Step #3: Change in Distance (Δd):

Step #4: Change in Time (Δt):

Step #5: Calculate the Speed:

Final Answer: 5 m/s

certified Physics and Maths tutorSolved Example

Problem: The Distance-Time Graph of an object shows a flat horizontal line at 5 meters for 10 seconds. What is the speed of the object?

Solution: 

Step #1: Observe the Graph,

    • The line is horizontal in the graph, so Distance does not change over time.

Step #2: Identify Two Points on the Graph:

    • At t1 = 0s, d1 = 5m.
    • At t2 = 10s, d2 = 5m.

Step #3: Change in Distance (Δd):

Step #4: Change in Time (Δt):

Step #5: Calculate the Speed:

Final Answer: 0 m/s

Frequently Asked Questions

Solution:

Use the formula: Speed = Distance ÷ Time. On a graph, calculate the slope by dividing the vertical change (distance) by the horizontal change (time).

Solution:

Calculate the area under the graph line. Use basic shapes like rectangles and triangles to measure the area, which gives you the distance.

A steeper line shows a higher speed — the object is moving faster.

Solution:

It means the object is stationary — it is not moving.

Solution:

Yes, when the slope changes or becomes curved (not shown in this example), it indicates acceleration or deceleration.

Solution:

  • Distance-time graph: Shows how far something has travelled
  • Velocity-time graph: Shows how fast it’s moving — area under graph = distance.

Practice regularly, look at real exam questions, and use worksheets. Pay attention to axes labels, slope changes, and units.

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