Part A. We are given that a car is pushed from rest to a final speed doing 5430 Joules of work. -
To determine the final velocity we will use the work and energy theorem which states that the work done is equal to the change in kinetic energy:
Since the car starts from rest this means that the initial kinetic energy is zero:
The kinetic energy is given by:
Substituting in the formula we get:
Now, we solve for the final velocity. First, we multiply both sides by 2 and divide both sides by the mass:
Now, we take the square root to both sides:
Now, we plug in the values:
Solving the operations:
Therefore, the final velocity is 2.04 m/s.
Part B. Now, we use the following formula for work:
Where "F" is the force and "d" is the distance.
Now, we set this equation equal to the work done by the force:
Now, we divide both sides by the distance "d":
Therefore, the force exerted is 187.2 Newton.