Question

What are the significance of velocity time graph

Answer 1

Answer:

1. Velocity time graph are used to describe the motion of objects which are moving in a straight line.

2.They can be used to show acceleration and to work out displacement.

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Answer 2

The velocity-time graph is significant for two reasons:-

1. The slope calculated from the graph gives the acceleration.
2. The area under the velocity-time graph indicates the displacement or the distance

• The velocity-time graph is one that is plotted with different values of velocities corresponding to its time values.
• The graph is plotted in a manner that the velocity lies in the Y-axis while the time is plotted in the X-axis.
• The area under a velocity-time graph tends to represent two quantities based on whether a vector quantity needs to be plotted or whether a scalar quantity is considered.
• The two quantities that are portrayed as the area under the graph are displacement and distance which are vector and scalar quantities respectively.
• The area of the graph is calculated based on the shape of the graph under plot and if it is linear then the area of the geometric shape formed is computed. In this case, velocity is constant so the area is equivalent to the distance.
• The area under the graph gives the distance or the displacement when all the instantaneous velocities along with its corresponding time periods are integrated together.
• When the velocity quantities are needed to be represented via both positive and negative values (with signs indicating directions) then the area gives the displacement as it is also a vector quantity.

• The slope of the graph corresponds to the acceleration of the body. If the magnitude of the slope is increasing it means that it depicts the increasing acceleration of the body.
• This is when the velocity continuously changes, in which case the slope will be steep. We know that the slope of any graph is given by:

                                                  $Slope= \frac{\Delta y}{\Delta x}$

• Here the velocity (v) values are the y coordinates and its corresponding instantaneous time (t) values are the x coordinates so slope becomes:

                                                $Slope= \frac{\Delta v}{\Delta t}$

• Since, we know that acceleration is defined to be the change in velocity with change in the time so we have:

                                           $Acceleration= \frac{\Delta v}{\Delta t}$

• Thus, the slope is given as the acceleration quantity. A negative slope indicates negative acceleration or retardation while a positive slope indicates positive acceleration in the opposite direction.

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