A cyclist comes to a skidding stop in 10 m. During this . . .

Question : A cyclist comes to a skidding stop in 10 m. During this process, the force on the cycle due to the road is 200 N and is directly opposed to the motion. (a) How much work does the road do on the cycle ? (b) How much work does the cycle do on the road ?

Doubt by Trishna 

Solution : 

After the application of brakes, the cycle stops after a distance of 10 m. 

So Displacement covered by the cycle,
S = 10 m
Force applied by the road on the cycle, 
F = 200 N

Both the Force and Displacement are in opposite direction. So θ=180°

a) Work done by the road on the cycle
W=FScos
θ
W=200×10×cos
180°

W=2000(-1) [∵cos180°=-1]
W=-2000 Joule 
W=-2000 J

b) Work done by the cycle on the road

As per Newton's Third Law
Action=-Reaction

So the magnitude of the force exerted by cycle on the road is 200 N

and Displacement of the road = 0 m
so 
W = FScos
180°
W = F(0)
cos180°
W = 0 Joule
W = 0 J