Question

Derive the relation x=v0t+

1

2

at2

for uniformly accelerated motion

with the help of velocity-time graph. ​

Answer 1

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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 = 1/2×Area of rectangle AEBD

= 1/2×AD×BD

= 1/2×t×at

= 1/2at^2

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

s = ut+ 1/2at