Question

A particle is moving with velocity ` vecv = k( y hat(i) + x hat(j)) `, where `k` is a constant . The genergal equation for its path is
A. `y^(2)=x^(2)+"constant"`
B. `y=x^(2)+` constant
C. `y^(2)=x+`constant
D. xy=constant

Answer 1

Correct Answer - a
`vecv=k(yhati+xhatj)`
`therefore v_(x)=(dx)/(dt)=ky`
`v_(y)=(dy)/(dt)=kx`
Dividing,
`(dy)/(dx)=(dy//dt)/(dx//dt(x)/(y)`
`y dy=x dx`
Integrating.
`inty dy=int x dx+` constant
`(y^(2))/(2)=(x^(2))/(2)+` constant
`y^(2)=x^(2)+` constant