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What is a velocity-time graph? Explain its.

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The geometrical relationship between the velocity of an object and the time taken by the object is called the velocity-time graph.

The velocity-time graph of an object can be drown by taking the time taken along the X-axis and the velocity along the Y-axis. The ratio of the velocity and the time taken will give the acceleration of the object. Therefore, the slope of the velocity-time graph gives the acceleration of the given object. That is, by using this graph one can find the acceleration of an object. The velocity-time graph under different conditions are shown below.

1. When the body is moving with uniform velocity

If the object moves at uniform velocity, the height of its velocity-time graph will not change with time. It will be a straight line parallel to the x-axis. We know that the product of velocity and time give displacement of an object moving with uniform velocity. The area enclosed by velocity-time graph and the time axis will be equal to the magnitude of the displacement.

To know the distance moved by the car between time t1 and t2 using the above figure, draw perpendiculars from the points corresponding to the time t1 and t2 on the graph. The velocity of v km/h is represented by the height AC or BD and the time (t2 – t1) is represented by the length AB. So, the distance s moved by the car in time (t2 – t1) can be expressed as

s = AC × CD = v(t2 – t1) = Area of the rectangle ABDC (shaded portion)

2. When the body is moving with uniform acceleration

In this case, the velocity-time graph for the motion of the car is shown in below figure. The nature of the graph shows that velocity changes by equal amounts in equal intervals of time. Thus, for all uniformly accelerated motion, the velocity-time graph is a straight line.

The area under the velocity-time graph gives the distance (magnitude of displacement) moved by the car in a given interval of time. If the car would have been moving with uniform velocity, the distance travelled by it would be represented by the area ABCD under the graph. Since the magnitude of the velocity of the car is changing due to acceleration, the distance s travelled by the car will be given by the area ABCDE under the velocity-time graph.

That is,

s = area ABCDE = area of the rectangle ABCD + area of the triangle ADE

3. When the body is moving with a variable acceleration

In the case of non-uniformly accelerated motion, velocity-time graphs can have any shape. In below Fig. (a) shows a velocity-time graph that represents the motion of an object whose velocity is decreasing with time while Figure (b) shows the velocity-time graph representing the non-uniform variation of velocity of the object with time.

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