For the work-energy theorem, the work done by the engine on the car is equal to the variation of kinetic energy of the car:
[tex]W= K_f-K_i=\frac{1}{2}mv_f^2 - \frac{1}{2} mv_i^2 [/tex]
where m=1167 kg is the mass of the car, [tex]v_i=10.0 m/s[/tex] is the initial speed and [tex]v_f=28.0 m/s[/tex] is the final speed.
Putting numbers into the equation, we find:
[tex]W= \frac{1}{2}(1176 kg)(28.0m/s)^2- \frac{1}{2}(1167 kg)(10.0 m/s)^2=4.0 \cdot 10^5 J [/tex]
