If some function say x varies linearly with time and we want to find its average value in a given time interval we can directly find it by `(x_(i)+x_(f))/(2)`. Here, `x_(i)` is the initial value of x and `x_(f)` its final value y co-ordinates of a particle moving in x-y plane at some instant are : `x=2t^(2)` and `y=3//2 t^(2)`. The average velocity of particle in at time interval from `t=1 s` to `t=2s` is :-

Options

A. `(8hat(i)+5hat(j)) m//s`
B. `(12 hat(i)+9hat(j)) m//s`
C. `(6hat(i)+4.5 hat(j)) m//s`
D. `(10 hat(i)+6hat(j)) m//s`

Answer

C

Explanation

`vec(v)=4t hat(i)+3that(j)" " ( :' x=at^(2) & y=3//2 t^(2))`
`v(1)=4hat(i)+3hat(j), v(2)=8hat(i)+6hat(j)`
`:. lt v gt =(12hat(i)+9hat(j))/2=(6hat(i)+4.5 hat(j)) m//s`