The velocity of an object is changing with time and relation is given by the following equation.
`v=2t+3t^(2)`
Calculate the position of the object from the origin at t = 2 s.
Assume particle to be at origin at t = 0

Explanation

We know, `v=(dx)/(dt)`
So position x is given by `x=intvdt`
`=int(2t+3t^(2))dt=(2t^(2))/(2)+(3t^(3))/(3)=t^(2)+t^(3)`
Substituting the values of t as 2 s, we get
`x=(2)^(2)+(2)^(3)=4+8=12m`
Position of object is 12 m from the origin at t = 2 s.