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

Answer 1

Correct Answer - D
` vec (v) = k (y hat (i) + xhat (j)) = v_(x) hat (i) + v_(y) hat (j) = (dx)/(dt) hat (i) + (dy)/(dt) hat (j) `,br. :. (x) / (dt ) = ky and :. (dy)/(dt) = kx` ,brgt `:. (dy)/(dx) = (x)/(y) rArr ydy = xdx rArr y^(2) = x^(2) + constant `