91Ó°ÊÓ

We know that the work done on an object is equal to the change in its kinetic energy (Work-Energy theorem). So, we can write the equation as: \[\text{{Work Done}} = \text{{Change in Kinetic Energy}} = \text{{Final Kinetic Energy}} - \text{{Initial Kinetic Energy}}\]Since the car starts from rest, the initial kinetic energy is zero. Therefore, the work done is equal to the final kinetic energy. The formula for kinetic energy is \(0.5 \times \text{{mass}} \times \text{{speed}}^{2}\). The work done and the mass of the car are given. From this we can derive an equation for the speed \(v\). \[5000 J = 0.5 \times 2.50 \times 10^{3} kg \times v^{2}\]Solving for \(v\), we get \(v = \sqrt{\frac{{5000 J}}{{0.5 \times 2.50 \times 10^{3} kg}}}\).

The work done by a force on an object is defined as the product of the force and the displacement of the object in the direction of the force (Work-Energy Theorem). Knowing the work done and the displacement, we can calculate the force as follows: \[\text{{Force}} = \frac{{\text{{Work Done}}}}{{\text{{Displacement}}}} = \frac{{5000 J}}{{25.0 m}}\]The above force is the average force exerted as the force might be variable because the car started from rest and reached a particular speed.