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20 12 mathematical model of Luwan district
When A and B turn off the self-charging device for the first time, it can be seen from Figure ① that 10m stops moving and the kinetic energy becomes 0, then only sliding friction does negative work F times 10m, which is equal to the original initial kinetic energy of 500J. According to the functional relationship, a functional relationship is generated. Namely: f× 10 = 500...①,

When the self-charging device is started for the second time, it can be seen from Figure ② that 6m stops moving and the kinetic energy becomes 0, so the negative work done by sliding friction F times 6m, which is equal to the initial kinetic energy minus the electric energy e charged into the battery according to the functional relationship, that is, f×6=500-E…

F=50(N) from ①, E = 500-50× 6 = 200 (j) into ②; Therefore, the electric energy charged into the battery for the second time is 200 J;

C from the above formula ②, fx=Ek0-E, it can be known that the amount of electric energy charged by the battery during charging is linear with the driving distance of the electric vehicle, but not proportional. So, c is wrong.

D. During the first movement, the electric vehicle is rubbed and decelerated at a uniform speed. In the second process, according to the kinetic energy theorem, it is obtained that the combination of -F and x =Ek-Ek0, and the combination of f and x =Ek0-Ek. According to mathematical knowledge, the slope of the image is equal to the resultant force. When the slope decreases gradually, the resultant force decreases and the acceleration decreases gradually. Therefore, the second electric vehicle decelerates at a gradually decreasing acceleration. Therefore, d is correct.

So choose ad.