how much work must be done in the car to slow it from 100km/h to 50km/h

where ∑Wext is the work done by the external forces on the system and ∑Wint is the work done by internal forces on the system. Newton's third law of motion gives you that ∑Fint=0, but the work done by internal forces may or may not be 0.

positive work increases the kinetic energy and negative work decreases the kinetic energy.
Work can be converted into kinetic energy and kinetic energy can be converted into work.

now coming back to our problem

[tex]v[/tex]1=[tex]50km/h=13.89m/s[/tex]

[tex]v[/tex]2=[tex]100km/h=27.78m/s[/tex]

Let us assume that average mass of the car(m) is [tex]1300kg[/tex] and ∑Wint=0J

Therefore, Work done(W)=ΔK

=K₂-K₁

=[tex]\frac{1}{2}m(v1)^{2}-\frac{1}{2}m(v2)^{2}[/tex]

=[tex]\frac{1}{2}*1300*(13.89)^{2}-\frac{1}{2}*1300*(27.78)^{2}[/tex]

=376.22KJ