Answer:
vf = 22.36[m/s]
Explanation:
First we must understand the data given in the problem:
m = mass = 800 [kg]
F = force = 20000[N]
dx = displacement = 10[m]
From newton's second we know that the sum of forces must be equal to the product of mass by acceleration.
[tex]F = m*a\\20000 = 800*a\\a = 20000/800\\a = 25 [m/s^2][/tex]
With the calculated acceleration, we can use the kinematics equations.
[tex]v_{f} ^{2} =v_{o} ^{2}+2*a*dx\\ v_{o} = initial velocity = 0\\a = acceleration = 25[m/s^2]\\dx= displacement = 10[m]\\[/tex]
The key to using this equation is to clarify that the initial velocity is zero since the body is at rest, otherwise the initial velocity would be an initial data.
[tex]v_{f} =\sqrt{2*25*10} \\v_{f} =22.36[m/s][/tex]
Another way of solving this problem is by means of the definition of work and kinetic energy, where work is defined as the product of the force by the distance.
W =F*d
W = 20000*10
W = 200000[J]
Kinetic energy is equal to work, therefore the value calculated above is equal to:
[tex]E_{k}=W =0.5*m*v_{f}^{2} \\200000=0.5*800*v_{f}^{2}\\v_{f}=\sqrt{\frac{200000}{0.5*800} } \\v_{f}=22.36[m/s][/tex]
