Respuesta :
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:
[tex]W=K_f-K_0[/tex]Since the car starts from rest this means that the initial kinetic energy is zero:
[tex]W=K_f[/tex]The kinetic energy is given by:
[tex]K=\frac{1}{2}mv^2[/tex]Substituting in the formula we get:
[tex]W=\frac{1}{2}mv_f^2[/tex]Now, we solve for the final velocity. First, we multiply both sides by 2 and divide both sides by the mass:
[tex]\frac{2W}{m}=v_f^2[/tex]Now, we take the square root to both sides:
[tex]\sqrt{\frac{2W}{m}}=v_f[/tex]Now, we plug in the values:
[tex]\sqrt{\frac{2(5430J)}{2.6\times10^3kg}}=v_f[/tex]Solving the operations:
[tex]2.04\frac{m}{s}=v_f[/tex]Therefore, the final velocity is 2.04 m/s.
Part B. Now, we use the following formula for work:
[tex]W=Fd[/tex]Where "F" is the force and "d" is the distance.
Now, we set this equation equal to the work done by the force:
[tex]Fd=5430J[/tex]Now, we divide both sides by the distance "d":
[tex]F=\frac{5430J}{29m}=187.2N[/tex]Therefore, the force exerted is 187.2 Newton.
