A particle is moving with velocity `vecv=K(y hat i+x hat j),` where K is a constant. The general equation for its path is

Options

A. xy= constant
B. `y^(2)=x^(2)+` constant
C. `y^(2)=x+` constant
D. `y=x^(2)+` constant

Answer

B

Explanation

`vecV=k(yhati+xhatj)`
`impliesV_(x)=(dx)/(dt)=ky`…….i
& `V_(y)=(dy)/(dt)=kx`….ii
using I and ii
`implies(dx)/(ky)=(dy)/(kx)impliesydy=xdx`
Integrating both sides
`implies(y^(2))/2=(x^(2))/2=` constant `impliesy^(2)=x^(2)+` constant