A particle moves on the xy-pane such that its position vector is given by `vec(r)=3t^(2) hati-t^(3) hatj`. The equation of trajectory of the particle is given by

Options

A. `3x^(2)+16 y =0`
B. `((3x)/2)^(4//3)+4y=0`
C. `(x/32)^(3//2) +y=0`
D. none of these

Answer

3

Explanation

`vec(r)=2t^(2) hati-t^(3) hatj`
`x=2t^(3) " " y=-t^(3)`
`(x/2)^(1//2)=t" " y=-(x/2)^(3//2)`
`(x/2)^(3//2) +y=0`