JEE Main 2024 Physics question
The relation between time 't' and distance 'x' is t = αx² + βx, where α and β are constants. The relation between acceleration (a) and velocity (v) is:
Answer: (C)
Solution
dt/dx = 2αx + β, so 1/v = 2αx + β. Differentiating with respect to t: −(1/v²)(dv/dt) = 2α(dx/dt) = 2αv, so a = −2αv³.