Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 → Introduction to Graphs ↓


Distance-Time Graphs


Understanding how distance-time graphs work is an important concept in math, especially when studying speed and motion. In this explanation, we'll look at what distance-time graphs are, how to read them, and what information they can provide about an object's motion. We'll also explore how to create these graphs and what significance their slopes hold. By the end of this article, you should feel comfortable interpreting and discussing distance-time graphs with ease.

What is a distance-time graph?

A distance-time graph is a simple graphical representation used to show the relationship between the distance travelled by an object and the time taken to cover that distance. The graph usually has two axes:

  • X-axis: This axis is horizontal and represents time. Time is usually measured in seconds, minutes, or hours.
  • Y-axis: This axis is vertical and represents distance. Distance can be measured in meters, kilometers, or other units.

The main idea is to plot time on the x-axis and distance on the y-axis. Each point on the graph corresponds to a specific time and the distance traveled at that time. By connecting these points, you get a line that shows the motion of the object over time.

How to read a distance-time graph

When you look at a distance-time graph, you should notice several important aspects. Let's take a look at these aspects one by one:

1. Slope of the graph

The slope or slope of the graph shows the speed of the object. A higher slope means the object is moving faster. This is because the steeper line shows a larger distance covered in a shorter amount of time.

If the slope is shallow or flat, it means the object is moving slowly, and traveling a short distance over a long period of time. If the graph is a horizontal line (perfectly flat), it indicates the object is not moving at all; its distance remains constant over time.

High speed (steep slope) Slow speed (shallow slope) Stopped (flat line)

2. Curve on the graph

Sometimes the line on a distance-time graph is not straight but curved. The curve shows whether the object is speeding up or slowing down. If the curve is getting steeper over time, the object is speeding up - it is speeding up. If the curve is getting less steep, the object is speeding up - it is slowing down.

Acceleration Recession

3. Position of points on the graph

Each point on the graph tells you the distance at a particular time. For example, if you have a point at (3, 15), it means that in 3 minutes, the object has traveled a distance of 15 meters.

(Time, Distance)

Drawing a distance-time graph

Let us learn how to plot a distance-time graph. Suppose we have the following data of the motion of an object:

Time (seconds) | Distance (meters) 0 | 0 1 | 2 2 | 4 3 | 6 4 | 8 5 | 10

To create a graph, follow these steps:

  1. Draw two perpendicular lines, one horizontal (x-axis) and one vertical (y-axis). Label the x-axis as time and the y-axis as distance.
  2. Mark a scale on each axis, making sure the interval is consistent and appropriate for the data points.
  3. Plot each time-distance pair as a point on the graph.
  4. Once all the points are marked, connect them with a line showing the movement of the object over time.
Time Distance(meters) 0 1 2 3 4 5 0 2 4 6 8 10

Understanding speed from distance-time graph

The concept of speed plays an important role in interpreting distance-time graphs. Speed is defined as the distance traveled per unit of time and is often expressed using the formula:

Speed = Distance / Time

When we look at a distance-time graph, speed can be determined by the slope of the line. The steeper the slope, the greater the speed. Here's how different line slopes represent different scenarios:

Constant speed: When the line on the graph is straight, it means that the speed of the object is constant. The constant slope of the line indicates the same ratio of distance and time throughout the journey.

Changing speed: If the graph line is curved, the speed is changing. If the line is getting steeper, the object is accelerating. If it is getting less steep, the object is slowing down.

Example problems

Example 1

A car travels 120 km in 2 hours. What is the speed of the car?

Solution:

Distance = 120 km Time = 2 hours Speed = Distance / Time = 120 km / 2 hours = 60 km/h

The speed of the car is 60 kilometres per hour.

Example 2

Draw a distance-time graph for the following data and describe the journey.

Time (minutes) | Distance (kilometers) 0 | 0 1 | 5 2 | 10 3 | 15 4 | 20 5 | 25 6 | 30 7 | 30 8 | 30 9 | 35 10 | 40
Time(minutes) Distance (km) 0 1 2 3 4 5 6 7 8 0 5 10 15 20 25 30

Solution:

The journey begins with a uniform speed for the first six minutes, in which a distance of 30 km is covered. Then the object stops and does not move for 2 minutes, thus maintaining the distance of 30 km. After this, the object starts the journey again and covers 5 km in 1 minute, then 5 km in the next minute and 40 km in 10 minutes.

Conclusion

Distance-time graphs provide a powerful way to visualize and analyze the motion of objects. By understanding how to interpret the slopes and curves of these graphs, one can easily estimate the speed, acceleration, and deceleration of an object. Creating graphs from given data is equally valuable, helping to solidify other mathematical concepts such as speed and time. As you become more comfortable with distance-time graphs, you will find that they are an essential part of understanding physics and mathematics at large.


Grade 8 → 7.3


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Distance-Time Graphs

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