Final Velocities In One Dimensional Elastic Collision
Final Velocities In One Dimensional Elastic Collision — the NEET Physics formula with its derivation, variables, validity constraints and worked solver.
Final Velocities in One-Dimensional Elastic Collision Valid only for perfectly elastic collisions in one dimension where both Kinetic Energy and Momentum are conserved. Set up Conservation of Momentum: m1v1i + m2v2i = m1v1f + m2v2f Set up Conservation of Kinetic Energy: 0.5m1v1i 2 + 0.5m2v2i 2 = 0.5m1v1f 2 + 0.5m2v2f 2 Rearrange momentum equation to group mass terms: m1(v1i - v1f) = m2(v2f - v2i) Rearrange energy equation using difference of squares: m1(v1i - v1f)(v1i + v1f) = m2(v2f - v2i)(v2f + v2i) Divide the energy equation by the momentum equation to find the relative velocity relationship: v1i + v1f = v2f + v2i Solve for v2f and substitute back into the momentum equation to isolate v1f. System must be isolated (no external forces during collision). Collision must be perfectly elastic (Coefficient of restitution = 1). Believing velocities simply swap regardless of mass (only true if masses are equal). Forgetting that velocity is a vector and signs indicate direction (e.g., negative for leftward motion). Applying this formula to inelastic collisions (where objects stick or deform).