Final answer:
You should downshift when starting up a hill and entering a curve as these conditions require more power and vehicle control. The concepts of kinetic and static friction explain smooth braking. Energy transformations, involving potential and kinetic energy, occur during motions like coasting and are affected by friction.
Step-by-step explanation:
The two special conditions that indicate you should downshift are when starting up a hill and entering a curve. In the first scenario, downshifting provides more power at lower speeds, which is helpful for climbing. In the second scenario, entering a curve, downshifting helps with control and stability of the vehicle. Both situations involve the principles of physics and vehicle dynamics.
When discussing the need to let up on the brake pedal to avoid a stop, this is explained by the relationship between static and kinetic friction. Kinetic friction occurs while the vehicle's wheels are moving, but when the vehicle comes to a complete stop, static friction takes over. If not adjusted correctly, the abrupt change from kinetic to static friction can cause the car to stop abruptly. Thus, easing off the brake pedal as the car comes to a stop transitions more smoothly from kinetic to static friction.
Concerning energy transformations such as in the case of the cyclist or the car coasting down a hill, potential energy is converted into kinetic energy as the object moves downhill. Due to friction, some of this kinetic energy is lost as heat, which is why the tires of a bicycle can get warm after coasting downhill. Lastly, when a car experiences non-negligible friction and coasts to a stop, it involves energy being transferred from potential to kinetic, and eventually being dissipated as heat during braking.
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