Answer :


Velocity–Time graph to derive the equations of motion.


Suppose the body travels a distance s in time t. In the above Figure, the distance travelled by the body is given by the area of the space between the velocity – time graph AB and the time axis OC,which is equal to the area of the figure OABC. Thus:


Distance travelled = Area of figure OABC


= Area of rectangle OADC + Area of triangle ABD


We will now find out the area of the rectangle OADC and the area of the triangle ABD.


(i) Area of rectangle OADC = OA × OC


= u × t


= ut ...... (5)


(ii) Area of triangle ABD = (1/2) × Area of rectangle AEBD


= (1/2) × AD × BD


= (1/2) × t × at (because AD = t and BD = at)


= (1/2) at2...... (6)


So, Distance travelled, s = Area of rectangle OADC + Area of triangle ABD


or s = ut + (1/2) at2
This is the second equation of motion. It has been derived here by the graphical method.


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