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Answer :

Answer:

Explanation:

The work-energy theorem says that the change in kinetic energy of a system is equal to the work done.

[tex]\frac{1}{2}mv^2_f-\frac{1}{2}mv^2_i=\Delta W^{}[/tex][tex]\frac{1}{2}m(v^2_f-v^2_i)=\Delta W^{}[/tex]

Now in our case

[tex]\begin{gathered} m=1079\operatorname{kg} \\ vf=\text{unknown} \\ v_i=3.00m/s \\ \Delta W=2.00\times10^5J \end{gathered}[/tex]

Therefore, the above equation gives

[tex]\frac{1}{2}(1079)(v^2_f-(3.00)^2^{}_{})=2.00\times10^5J[/tex]

Now we need to solve for v_f .

Mutlipying both sides by 2 gives

[tex](1079)(v^2_f-(3.00)^2_{})=2.00\times10^5\times2[/tex]

dividing both sides by 1079 gives

[tex](v^2_f-(3.00)^2_{})=\frac{2.00\times10^5J}{1079}\times2[/tex]

Finally, adding 3.00^2 to both sides gives

[tex]v^2_f=\frac{2.00\times10^5J}{1079}\times2+3.00^2[/tex]

Finally, simplifying the right-hand side gives

[tex]v^2_f=379.71[/tex]

taking the square root of both sides gives

[tex]\boxed{v_f=19.49m/s}[/tex]

Hence, the final speed of the car is 19.49 m/s.