then the kinetic energy stays t (11) SEP Use Mathematics A shopping velocity of the 28-kq eventually it slows to a stop release is 3.5m/s and it travels a distance of 6.0 meters stopping, determine the magnitude of the of the on the before

To determine the magnitude of the force acting on the shopping cart before it comes to a stop, we can use the work-energy principle. The work done by the force on the cart will be equal to the change in its kinetic energy.<br /><br />Given information:<br />- Mass of the shopping cart: 28 kg<br />- Initial velocity of the cart: 3.5 m/s<br />- Distance traveled before stopping: 6.0 meters<br /><br />Step 1: Calculate the initial kinetic energy of the cart.<br />Kinetic energy (KE) = (1/2) × mass × velocity^2<br />KE = (1/2) × 28 kg × (3.5 m/s)^2<br />KE = 0.5 × 28 × 12.25<br />KE = 171.5 J<br /><br />Step 2: Calculate the final kinetic energy of the cart when it comes to a stop.<br />Final kinetic energy = 0 J (since the cart comes to a stop)<br /><br />Step 3: Calculate the work done by the force on the cart.<br />Work done = Change in kinetic energy<br />Work done = Final kinetic energy - Initial kinetic energy<br />Work done = 0 J - 171.5 J<br />Work done = -171.5 J<br /><br />Step 4: Calculate the magnitude of the force acting on the cart.<br />Work done = Force × Distance<br />Force = Work done / Distance<br />Force = -171.5 J / 6.0 m<br />Force = -28.58 N<br /><br />The negative sign indicates that the force is acting in the opposite direction to the motion of the cart. Therefore, the magnitude of the force acting on the shopping cart before it comes to a stop is 28.58 N.