the initial velocityof a particle along x axis is u at t=0 x=0 and its acceleration is given by a = 2x then whats the correct equation for v^2 = u^2 + 2as

v² = u² + 2x²

Explanation:

v² = u² + 2as is only valid for constant acceleration. Here, the acceleration is a function of position. We can find the function of velocity by integrating. Acceleration is the derivative of velocity with respect to time:

a = 2x

dv/dt = 2x

Apply chain rule:

dv/dt = dx/dt * dv/dx

dv/dt = v * dv/dx

Therefore:

v dv/dx = 2x

Separate the variables and integrate:

v dv = 2x dx

½ v² |ᵤᵛ = x² |₀ˣ

½ (v² - u²) = x²

v² - u² = 2x²

v² = u² + 2x²