The simple solution is as follows: let f=K*V*V, and k be the proportional coefficient. According to the momentum theorem, there is Fdt=mdv, provided that (F-K*V*V)dt=m*dV, and dt=[m/(F-K*V*V)]*dV is obtained by separating variables, and both sides can be integrated separately. The integral method is simply to divide the right side by the sum of two scores, which should be very simple for college students.
The answer is t=(mV/2F)*ln(V+v)/(V-v) as for k, it depends on f=F when the maximum speed Vm is reached and K=F/(V*V). Finally, by substituting V=Vm/2, we can get the time t=0.5ln3 *mV/F, where V is the maximum speed Vm (rough calculation, I don't know if the answer is right).
The above equation is the relationship between v and t,
When solving the distance, vdt=ds can be integrated. The processing method is as follows: Because the equation given above is t=f(V) and its inverse function is difficult to find, it is necessary to transform vdt=ds.
Method 1: Multiply the differential dV of the left and right speeds at the same time and move dt to the right. Then, according to dV/dt=a=(F-K*V*V)/m, [mV/(F-K*V*V)]dV=ds is simplified. At this time, both sides can merge at the same time. The scoring method is multiplied by the differential on the left.
Method 2: directly differentiate the left and right sides according to t=f(V) to get dt=g(V)dv, and then bring it into vdt=ds for integration.
Make your own specific process, don't ask if you don't understand.