Final answer:
Coasting down a hill with the clutch in a standard transmission vehicle would generally Maintain current speed, but in reality, the car would usually slow down due to friction and air resistance. Energy conversion occurs when the car coasts over a crest, where kinetic energy is turned into potential energy and then back into kinetic energy, with thermal energy generated by friction.
Step-by-step explanation:
If a vehicle has a standard transmission, coasting down a hill with the clutch pushed "IN", it will Maintain current speed if there are no other external forces like wind resistance or additional friction being applied. As the car coasts, kinetic energy is preserved unless other forces act on it to slow it down or speed it up. However, in reality, due to air resistance and rolling resistance, the car would slowly lose speed.
In the scenario where a car running out of gas coasts down a hill and over a crest into a gas station, the car's kinetic energy converts into potential energy as it ascends the crest and back into kinetic energy as it descends. During this process, thermal energy is generated due to friction, which leads to a loss in mechanical energy. If friction were negligible, the conservation of mechanical energy would allow us to predict the height that the car could reach based on its initial speed.