A particle performs linear S.H.M. At a particular instant, velocity of the particle is ' u ' and acceleration is ' ' while at another instant, velocity is ' v ' and acceleration is ' ' (0 ) . The distance between the two positions is

Step-by-step solution

When velocity is u and acceleration is , let the position of particle be x ₁ . When velocity is v and acceleration is , let the position of particle be x₂ . If is the angular frequency then, = ^2 x₁ and = ^2 x₂ + = ^2 ( x ₁+ x ₂ ) ...(i) Also, velocity of particle at particular instant can be given as, aligned & u^2= ^2 A^2- ^2 x₁^2 & and v^2= ^2 A^2- ^2 x₂^2 & i.e., v^2-u^2= ^2 (x₁^2-x₂^2 ) & v^2-u^2= ^2 (x₁-x₂ ) (x₁+x₂ )...(ii) aligned from equation (i) we get aligned & v^2-u^2= (x₁-x₂ )( + ) & x₁-x₂= v^2-u^2 + &