Graphical Representation of Motion
Motion of an object can be represented graphically. There are three types of graphs
• Displacementtime graph,
• Velocitytime graph and
• Accelerationtime graph.
Displacementtime graph provides information about the motion of an object.
• The slope of displacementtime graph gives the velocity.
• When displacementtime graph is straight line parallel to time axis then the object is said to be stationary.
• In case of graph is straight line but not parallel to time axis then object is said to have uniform velocity.
Velocitytime graph slope gives the acceleration.
• In case an object is moving with uniform velocity, the graph will be a straight line parallel to time axis.
• In case velocitytime graph is a straight line but not parallel to time axis then the velocity of object is increasing at uniform rate.
Accelerationtime graph gives the information about the types of acceleration that means positive, negative or zero.
• The area under accelerationtime graphs gives the velocity.
• When the acceleration time graph coincides with the time axis then object is said to be either moving with uniform velocity or is at rest.
• If the accelerationtime graph is a straight line but not parallel to time axis then object is said to have variable velocity and acceleration.
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Q1
What does the below graph indicates about the motion of a car?
Marks:1Answer:
In a distancetime graph, a straight line parallel to the time axis indicates that the car is not moving as it does not change its position with respect to time.

Q2
Find out the acceleration of the graph line AC, given below.
Marks:2Answer:
The slope of the graph line AC, i.e., (AB/BC) gives the acceleration.

Q3
From the velocitytime graph given below, calculate:
(i) Acceleration in the region AB.
(ii) Deacceleration in region BC.
(iii) Distance covered in the region ABCE.
(iv) Average velocity in region CED.Marks:5Answer:
By using the velocitytime graph,
(i) Acceleration = Slope of graph line AB
= BF/AF = (14 m/s)/12 s
= 1.16 ms^{2}
(ii) Deacceleration = Slope of graph line BC
= BG/GC = (8 m/s)/4 s
=  2 ms^{2 } 
Q4
What do you understand by the term slope of the line? Explain with the help of clear diagram.
Marks:2Answer:
The slope of a line is defined as the change in the ycoordinate divided by the corresponding change in the xcoordinate, between two distinct points on the line.
It can be calculated as
i.e., slope of graph = ∆y/∆x.

Q5
Give a characteristic of a straight line graph.
Marks:1Answer:
The main characteristic of a straight line graph is given below:
1. In a straight line graph, two variables are directly proportional to each other i.e., if one quantity increases then the other quantity also increases.