Chapter 8 - Potential Energy and Conservation of Energy - Problems - Page 205: 38b

$v = 12.6m/s$

Finding the kinetic energy at $U(J) = 0$: $E_0=E_A$ $K_0 + U_0 = K_A + U_A$ $K_0 = K_A + U_A - U_0$ $K_0 = 12J + 4J - 0J$ $K_0 = 16J$ Using $K_0$ to find the speed at $x=6.5m$ $K_0 = \frac{mv^2}{2}$ $2K_0 = {mv^2}$ $\frac{2K_0}{m} = {v^2}$ $v =\sqrt \frac{2K_0}{m} $ $v =\sqrt \frac{2 \times 16J}{0.2kg} $ $v = 12.6m/s$