VVELOCITY TIME GRAPH

VELOCITY TIME GRAPH:
Graphs may be used to illustrate the variation of velocity of an object with time. Such graphs are called velocity- time graphs

Zero Acceleration or uniform velocity graph:

When the velocity of the car is constant, then the velocity time graph is a horizontal straight line as shown in fig (a).

                                                                                                                             
Uniform Acceleration Graph:
When the car moves with constant acceleration, the velocity time graph is a straight line which rises the same height for equal intervals of time (Fig (b).                                                                                                                           
Variable Acceleration Graph:

The slope of graph determines the average acceleration. The greater the slope or steepness the greater is the acceleration.

            If the change in velocity with time is not uniform then the velocity time graph is a curve. The acceleration at any instant ‘t’ at any point ‘A’ can be determined by the slope of the tangent at the point ‘A’. fig (c)                                                       
                                                                                                                                                                                    
Distance: 
Distance covered by the body is numerically equal to the area under the velocity time graph and the time axis 

For example:

Fig (a) shows that the object moves at constant velocity v for time t

            The distance covered by object is v ´ t

This distance can be found by velocity time graph. This area is shown shaded in fig (a) and is equal to v ´ t.

in fig (b) Velocity of object increases uniformly from 0 to v in time ‘t’.

            The magnitude of its average velocity is,
            
Distance covered = average velocity ´ time

To find area:

            Area under velocity time graph is equal to the area of the triangle shaded in fig (b)

            Its value is equal to 

Conclusion:

            Considering the above two examples it is a general conclusion that.

“The area between the velocity time graph and the time axis is numerically equal to the distance covered by the body”

Velocity - Time Graph

1. The gradient of the velocity-time gradient gives a value of the changing rate in velocity, which is the acceleration of the object.
2. The area below the velocity-time graph gives a value of the object's displacement.

Analysing Velocity-Time Graph

1. When analysing velocity-time graph, always keep in mind that the gradient of the graph is equal to the acceleration of the graph.
2. If the gradient is constant, then the acceleration is constant. If the gradient increase, then the acceleration increase and etc.
3. Table below shows a few cases of velocity-time graph for different types of motion.

Converting a Velocity-Time graph to Acceleration-Time graph

1. In order to convert a velocity-time graph to acceleration time graph, we need to find the gradient of the velocity time graph and plot it in the acceleration-time graph.