Graphical Representation of Motion

Motion of an object can be represented graphically. There are three types of graphs-
•    Displacement-time graph,
•    Velocity-time graph and
•    Acceleration-time graph.
Displacement-time graph provides information about the motion of an object.
•    The slope of displacement-time graph gives the velocity.
•    When displacement-time 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.

                                                     

Velocity-time 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 velocity-time graph is a straight line but not parallel to time axis then the velocity of object is increasing at uniform rate.

                                                        

Acceleration-time graph gives the information about the types of acceleration that means positive, negative or zero.
•    The area under acceleration-time 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 acceleration-time 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:1
    Answer:

    In a distance-time 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.

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  • Q2

    Find out the acceleration of the graph line AC, given below.

    Marks:2
    Answer:

    The slope of the graph line AC, i.e., (AB/BC) gives the acceleration.


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  • Q3

    From the velocity-time graph given below, calculate:

    (i) Acceleration in the region AB.
    (ii)
    De-acceleration in region BC.
    (iii)
    Distance covered in the region ABCE.
    (iv)
    Average velocity in region CED.

    Marks:5
    Answer:


    By using the velocity-time graph,

    (i)
    Acceleration = Slope of graph line AB
    = BF/AF = (14 m/s)/12 s

    = 1.16 ms-2

    (ii)
    De-acceleration = Slope of graph line BC
    = BG/GC = (-8 m/s)/4 s

    = - 2 ms-2

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  • Q4

    What do you understand by the term slope of the line? Explain with the help of clear diagram.

    Marks:2
    Answer:

    The slope of a line is defined as the change in the y-coordinate divided by the corresponding change in the x-coordinate, between two distinct points on the line.

    It can be calculated as

    i.e., slope of graph = ∆y/∆x.

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  • Q5

    Give a characteristic of a straight line graph.

    Marks:1
    Answer:

    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.

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