A shopping cart that has an inertia of \(12 \mathrm{~kg}\) when empty is loaded with \(38 \mathrm{~kg}\) of groceries. A child pushing the loaded cart loses control, and the cart rolls into a concrete lamppost, which sustains no damage. The cart is moving at \(2.0 \mathrm{~m} / \mathrm{s}\) when it strikes the lamppost, and the groceries all crash forward on impact, moving the center of mass forward by \(0.10 \mathrm{~m}\) before everything comes to a halt. What are 

\((a)\) the average force exerted by the post on the cart-groceries system,

(b) the work done by the post on the system, and

(c) the change in kinetic energy of the system's center of mass?