Question

A particle is moving with velocity v = k(yi +xj) ,where k is a constant . the general equation for its path is [AIEEE:2010]​

Answer 1

Given :- V = kyi+ kx j

• dx/dt = ky
• dy/dt = kx
• dy/dx = dy/dt ×dt/dx = kx/ky
• ydy =xdx

Integration and using , ∫Xⁿdx = Xⁿ⁺¹/n+1, we have

• ∫ydy =∫ xdx
• y²/2 = x²/2
• y²=x²
• y² = x²+c Is general equation for its path