he kinetic energy P Use Mathematics A shopping cart is pushed and rel entually it slows to a stop.If the velocity of the 28-kg ease is 3.5m/s and it travels a distance of 6.0 meters pping determine the magnitude of the friction on th

To determine the magnitude of the friction on the shopping cart, we can use the work-energy theorem. The work done by the friction force will be equal to the change in kinetic energy of the shopping cart.<br /><br />Given information:<br />- Mass of the shopping cart (m) = 28 kg<br />- Initial velocity (v_i) = 3.5 m/s<br />- Final velocity (v_f) = 0 m/s (since the cart comes to a stop)<br />- Distance traveled (d) = 6.0 meters<br /><br />Step 1: Calculate the initial kinetic energy of the shopping cart.<br />Kinetic energy (KE) = (1/2) * m * v_i^2<br />KE = (1/2) * 28 kg * (3.5 m/s)^2<br />KE = 245 J<br /><br />Step 2: Calculate the change in kinetic energy.<br />Change in kinetic energy = Final kinetic energy - Initial kinetic energy<br />Change in kinetic energy = 0 J - 245 J = -245 J<br /><br />Step 3: Calculate the work done by the friction force.<br />Work done by friction = Change in kinetic energy<br />Work done by friction = -245 J<br /><br />Step 4: Calculate the magnitude of the friction force.<br />Work done by friction = Force of friction * Distance traveled<br />-245 J = Force of friction * 6.0 m<br />Force of friction = -245 J / 6.0 m<br />Force of friction = -40.83 N<br /><br />The negative sign indicates that the friction force is acting in the opposite direction to the motion of the shopping cart. Therefore, the magnitude of the friction force is 40.83 N.