You need to determine the best option to push a small cart from 0 to 8 m/s. Two options are offered. The first one implies a mass of 100 kg, a push force of 200 N and a friction coefficient 5 times the velocity (friction force approximate by 5 v). This system will cost 1$ for every second of use. The second one, the mass is 150 kg, the push force is 300 t N (t is the time in second), and the friction is the same as the other option. However, this one only cost 1.5$ per second of use. A) Solve the equations of both options. B) Build a table with the velocity and the cost for both option for the first 5 second of the run. C) Which option (with explanation) is the cheapest to reach 8 m/s? D) Which is the viable option if your employer now ask that the system only reaches 4 m/s? Why? Hints: Use Newton's second law to build the equations (Velocity in one dimension)