Question

Derive the equations of motion by graphical method s=ut +1/2at^2​

Answer 1

Answer:

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

=21at2

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

s=ut+21at2