Question

Derive the equation

$s = ut + 1 \div 2 \: at^{2}$
​

Answer 1

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 -------(i)

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

= (1/2) × t × at

= (1/2) at2 --------(ii)

From Eq. i and ii

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

S= ut + (1/2) at^2

This is the second equation of motion. It has been derived here by the graphical method.

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