📈 Acceleration as a Function of Distance – Motion in One Dimension | JEE Physics | Doubtify JEE 🧮 Question: The distance x covered by a particle in one-dimensional motion varies with time t as: x² = at² + 2bt + c . If the acceleration of the particle depends on x as x⁻ⁿ , where n is an integer, what is the value of n ? 🖼️ Question Image: ✅ Detailed Concept & Solution: This is a JEE-level conceptual problem involving the relation between distance, velocity, and acceleration — with a twist of functional dependence. We are given: x² = at² + 2bt + c — (1) To find acceleration and its dependency on x , let’s differentiate both sides of equation (1): Differentiate w.r.t. time t : 2x(dx/dt) = 2at + 2b ⇒ v = dx/dt = (at + b)/x — (2) Now differentiate velocity v w.r.t time to find acceleration: a = dv/dt = d/dt[(at + b)/x] Use quotient rule: a = [a·x - (at + b)(dx/dt)] / x² Plug dx/dt = (at + b)/x from (2): a = [a·x - (at + b)·((at + b)/x)] / x² ⇒ ...