An object thrown in the air has a velocity after t seconds that can be described by v(t) = −9.8t + 31 (in meters/second) and a height h(t) = −4.9t2 + 31t + 45 (in meters). The object has mass m = 4 kilograms. The kinetic energy of the object is given by K = 1 2 mv2, and the potential energy is given by U = 9.8mh. Enter an expression for the total kinetic and potential energy K + U as a function of time. What does this expression tell you about the energy of the falling object? Complete the explanation. K+U= () joules

Since the sum is (U/K/a single variable/a constant), this means that the energy of the object is constant and that as it (gains/loses) kinetic energy by falling, it ( gains/loses) the same amount of potential energy.