Graphs Questions

A graph is a way of showcasing the relationship between two quantities. The graph represents the relation between two parameters, where one parameter varies as a result of a change in the other. It is one of the easy and interactive ways of representing information. In Physics graphs play a major role in explaining two parameters. A graphical representation of any data can give a qualitative relation of the variables without the need to perform any further calculations. Graphs can show how dependent and independent variables vary.

Terms used in graphs are:

1. Independent variable
2. Dependent variable

The independent variable is a variable whose value is independent of other variables. A variable that alters due to the change in the independent variable is known as a dependent variable.

There are three types of graphs, they are:

• Displacement – time (d-t) graph
• Acceleration-time (a-t) graph
• Velocity-time (v-t) graph

These graphs are ideally to learn the motion of the body.

Displacement – Time graph

Displacement is defined as the change in the position of an object. In the displacement time graph, displacement is a dependent variable, and time is an independent variable. Displacement is indicated on the y-axis, whereas time is on the x-axis. This graph is also called the Position-time graph.

Condition 1: When the object is not moving for some time and slope results zero, this indicates that the object has zero velocity.

Condition 2: When the object moves at constant velocity and increases with time, this indicates that the slope remains positive and constant.

Condition 3: When parameters like displacement, acceleration, and velocity are constant. The slope of the graph increases with time.

Note: When the slope is a positive value, it indicates that the motion is in the positive direction.

When the slope is a negative value, it indicates that the motion is in the negative direction. When the slope is zero, it indicates that the object is at rest.

The slope for the displacement time graph is given by the formula: Δd/Δt.

Velocity-Time graph

Velocity is defined as the rate at which an object changes its position. In the velocity-time graph, velocity is a dependent variable and time is an independent variable. Velocity is indicated on the y-axis, whereas time is on the x-axis. Velocity time graph slope is given by the formula: Δv/Δt.

Note: Rapid change in the velocity is given by the steep slope. The slow change in velocity is given by the shallow slope. When the slope is negative, the acceleration is negative. When the slope is positive, the acceleration is positive.

Acceleration-Time graph

Acceleration is the rate of change of the velocity of an object with respect to time. In the acceleration time graph and time is an independent variable. Acceleration is indicated on the y-axis, whereas time is on the x-axis. The graph of acceleration time slope is referred to as jerk. The acceleration time graph slope is given by the formula: Δa/Δt.

Note: The motion of the object is said to have constant acceleration if the slope is zero. The change in velocity is given by the area under the acceleration-time graph.

Important Graphs Questions with Answers

1. The rate at which an object changes its position ____

1. Displacement
2. Velocity
3. Acceleration
4. Altitude

Answer: b) Velocity

Explanation: Velocity gives the rate at which an object changes its position.

2. Graph is a ____ dimensional drawing.

1. One
2. Two
3. Three
4. Four

Answer: b) Two

Explanation: Graph is a two-dimensional drawing

3. Fill in the blanks: In the displacement-time graph, the slope is equal to ____

Answer: velocity

Explanation: Velocity gives the rate at which an object changes its position.

4. Which of the graphs represents that acceleration, velocity, and displacement are constant, and the slope of the graph increases with time?

1. 
2. 
3. 
4. None of the options

Answer: a)

Explanation: Graph one represents that acceleration, velocity and displacement are constant, and the slope increases with time.

5. State true or false: velocity is the independent variable in the velocity-time graph.

1. TRUE
2. FALSE

Answer: b) FALSE

Explanation: In the velocity-time graph, velocity is a dependent variable.

6. Δa/Δt gives the slope of _____

1. Displacement – time (d-t) graph
2. Velocity-time (v-t) graph
3. Acceleration-time (a-t) graph
4. None of the option

Answer: c) Acceleration-time (a-t) graph

7. Rapid change in velocity is given by

1. Shallow slope
2. Steep slope
3. No slope
4. None of the options

Answer: b) Steep slope

Explanation: The rapid change in velocity is represented by a steep slope.

8. Fill in the blanks: If the slope is zero, the motion is said to have ____ acceleration.

1. Increasing
2. Decreasing
3. Constant
4. None of the options

Answer: c) Constant

9. Jerk is

1. The slope of the v-t graph
2. The slope of the d-t graph
3. The slope of the a-t graph
4. None of the option

Answer: c) The slope of the a-t graph.

Explanation: The slope of the a-t graph is known as a jerk.

10. Choose the correct answer: In the d-t graph, which is the independent variable

1. Displacement
2. Time

Answer: b) Time

Explanation: In the d-t graph, time is the independent variable.

Read more: Velocity-time graph.

Practice Questions

1. Define velocity, acceleration, and displacement.
2. Explain the slope formula in the v-t graph.
3. What is the formula to find the slope for the displacement time graph?.
4. What are the three types of graphs?
5. Explain two features of the graph.

Watch the video below to understand the velocity-time graph and displacement-time graph.