A body of mass 8 kg is moved by a force F=3 x ~N , where x is the distance covered. Initial position is x=2 ~m and the final position is x=10 ~m . The initial speed is zero. The final speed is

Step-by-step solution

aligned & Force, F=m a=m d v d t & aligned 3 x & =8 d v d x d x d t 3 x & =8 v d v d x 3 x d x & =8 v d v aligned aligned Integrating both sides aligned 3 [ x^2 2 ]₂¹⁰ & =8 [ v^2 2 ]₀^v 3 2 [10^2-2^2 ] & =4 v^2 3 2 96 & =4 v^2 v & =6 ~m / s aligned