All About Distance-Time Graph
Distance-time graphs show how far an object has travelled in a designated period of time. The graph shows distance versus time and is made up of a simple line graph.
1. On the Y-axis, the distance is plotted.
2. On the X-axis, time is plotted.
Distance-time graphs show the speed of a vehicle changing along curved lines.
The Importance of Distance - Time Graphs
In studying the motion of bodies, we deal with distance-time graphs. A distance-time graph representing the motion of a body is obtained when we plot the data for distance and time for a body on a rectangular graph.
Distance vs. Time Definition
During the study of distance-time graphs, the three most critical components are time, speed, and distance. The vertical Y-axis of a graphical representation is the vertical time axis, while the horizontal X-axis is the horizontal distance axis. Then, once the axes are determined, it is easy to plot the values on the graph.
As the distance versus time graph shows, we can see the different variations of the body's movement. For instance, when a graph plots as a straight line, this indicates that the body is moving at a fixed (or constant) speed.
Time Distance Graph Worksheet.
To help students gain a better understanding of the topic, we have compiled some worked-out mathematical problems.
Consider the following graph that shows Ralph's entire journey. Here are the results.
He covered a total distance.
He remained stationary for a period of time.
He travelled at an average speed of 17:15 to 17:45 (kilometers per hour).
By looking at the axis, it appears that Ralph first travelled 25 km, rested, and then returned home. Therefore, the total distance he travelled was 25km + 25km = 50 km.
Ralph was in the station for one box's duration, which is clear from the graph. Additionally, from the axis, it is clear that two boxes total equal 15 minutes. The time spent stationary would be 15/2 = 7.5 minutes.
First, you must estimate the gradient of the graph from 17:15 to 17:45 (30 minutes or 0.5 hours) to calculate the average speed between the points. As you can see, he increased his speed by five kilometers until he reached 25 kilometers. In total, he traveled 20 kilometers. Since the gradient is 20/0.5, his speed is 40 km/h.
E-learning platforms like Vedantu can help you learn more about distance time graphs. It is easy to learn such topics without any hassle if you have expert suggestions, mock exam question papers, and lucid explanations. Additionally, live classes and question-and-answer sessions with experts will help you to better prepare for your final exam.
FAQs on Distance Time Graph
1. What is a distance-time graph and what does it show?
A distance-time graph is a visual tool used in Physics to represent the motion of an object. It plots the total distance an object has travelled against the time it has taken. The distance is plotted on the vertical axis (Y-axis), and time is plotted on the horizontal axis (X-axis). This graph provides a clear picture of an object's journey, showing how its distance from a starting point changes over a period.
2. What does the slope (or gradient) of a distance-time graph represent?
The slope of a distance-time graph represents the speed of the object. A key principle to remember is:
- A steeper slope indicates a higher speed, meaning the object is covering more distance in less time.
- A gentle slope signifies a slower speed.
- A zero slope (a flat, horizontal line) means the object is stationary, as its distance is not changing over time.
3. How is an object's speed calculated from its distance-time graph?
You can calculate an object's speed by determining the gradient of its line on the graph. For an object moving at a constant speed (a straight line), the formula is:
Speed = Total Distance Covered / Total Time Taken.
To find this, you can pick two points on the line and divide the change in distance (the vertical change) by the change in time (the horizontal change).
4. How do you draw a distance-time graph from a set of data?
To draw a distance-time graph, follow these steps:
- Draw and label the axes: The horizontal X-axis for Time and the vertical Y-axis for Distance.
- Choose a suitable scale for both axes that accommodates all your data values.
- Plot the data points. For each time value, mark the corresponding distance value on the graph.
- Join the plotted points with a line. A straight line indicates uniform motion, while a curve indicates non-uniform motion.
5. What do different shapes of lines on a distance-time graph indicate about an object's motion?
The shape of the line on a distance-time graph reveals the nature of the object's motion:
- A straight horizontal line means the object is at rest (stationary).
- A straight line sloping upwards indicates the object is moving at a constant speed (uniform motion).
- A curved line shows that the object's speed is changing, meaning it is undergoing acceleration (if the curve gets steeper) or deceleration (if the curve flattens).
6. What is the key difference between a distance-time graph and a displacement-time graph?
The primary difference is the quantity measured on the vertical axis. A distance-time graph plots the total path length covered, which can never decrease. Therefore, its slope (representing speed) is always positive or zero. In contrast, a displacement-time graph plots the object's change in position from its starting point. Since displacement has a direction, this graph's slope can be negative if the object returns towards its origin. The slope of a displacement-time graph gives velocity, not speed.
7. Can the line on a distance-time graph ever be vertical or slope downwards?
No, a line on a distance-time graph cannot be vertical or have a negative (downward) slope. Here's why:
- A vertical line would imply that an object covers a certain distance in zero time, which suggests infinite speed. This is physically impossible.
- A downward-sloping line would mean the total distance travelled by the object is decreasing. Distance, being a scalar measurement of the total path covered, can only increase or stay constant.
8. What are some real-world examples that can be represented by a distance-time graph?
Distance-time graphs are excellent for visualising everyday motion, such as:
- The journey of a bus travelling between stops, showing periods of acceleration, constant speed, and being stationary.
- Tracking the progress of a sprinter in a 100m race, which would likely show a steepening curve as they accelerate.
- A simple representation of a walk to the park and back, where the distance increases on the way there and increases further on the way back (as total distance is cumulative).
