Question

Establish the formula S=ut+ 1/2 at ² by graphically.​

Answer 1

Consider the velocity-time graph of a body shown in the figure. The body has an initial velocity u at a point A and then its velocity changes at a uniform rate from A to B in time t. In other words, there is a uniform acceleration a from A to B, and after time t its final velocity becomes v which is equal to BC in the graph. The time t is represented by OC.

Suppose the body travels a distance s in time t. In the figure, the distance traveled 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 traveled = Area of figure OABC

= Area of rectangle OADC + area of triangle ABD

Now, we will find out the area of rectangle OADC and area of triangle ABD.

(i) Area of rectangle OADC=OA×OC

=u×t

=ut

(ii) Area of triangle ABD= 21 ×Area of rectangle AEBD= 21 ×AD×BD= 21

×t×at= 21 at 2

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

s=ut+ 21 at 2solution

Answered By=shreyash. ...

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