Final answer:
To determine the initial velocity of the cart, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the cart is 110 J and the final velocity is 8.0 m/s. Using the equation for kinetic energy, we can solve for the initial velocity of the cart.
Step-by-step explanation:
To determine the initial velocity of the cart, we can use the work-energy theorem. The work done on an object is equal to the change in its kinetic energy. In this case, the work done on the cart is 110 J and the final velocity is 8.0 m/s. The initial kinetic energy of the cart is zero.
Let's assume the initial velocity of the cart is 'v'. The initial kinetic energy of the cart is 0.5 * (4 kg) * v^2. The final kinetic energy of the cart is 0.5 * (4 kg) * (8.0 m/s)^2.
Setting the initial kinetic energy equal to the final kinetic energy, we can solve for 'v'. 0.5 * (4 kg) * v^2 = 0.5 * (4 kg) * (8.0 m/s)^2. Simplifying the equation, we get v^2 = (8.0 m/s)^2. Taking the square root of both sides, we find that the initial velocity of the cart is 8.0 m/s.