Question

to prove 2nd equation of motion by graphical method
​

Answer 1

Answer

Suppose a body travels a distance "s" in time "t".

The distance travelled by the body is given by the area of the space between the velocity time graph AB and the axis OC, which is equal to the area of the Fig (please refer to attachment) OABC.

Distance travelled = area of triangle ABD + area of rectangle OADC

Area of rectangle OADC = l × b

= OC × OA

= t × u

= tu

= ut ........... ( i )

Now,

Area of triangle ÷ 1/2 × b × h

= AD × BD

= 1/2 × t × at

$= \: \frac{1}{2} a {t}^{2} ........( \: ii \: )$

Adding both the eq ( i ) and eq ( ii )

$\implies \: s \: = \: \: ut \: + \: \frac{1}{2} a {t}^{2}$