Final answer:
Vehicles slow down going uphill because their engines need to work against gravity, requiring more power to maintain speed. Vehicles accelerate downhill as gravity aids in their motion, converting potential to kinetic energy. Realistically, energy losses prevent vehicles from reaching their theoretical maximum velocity.
Step-by-step explanation:
Vehicles tend to slow down when going uphill and pick up speed when moving downhill due to the influence of gravitational forces. When a vehicle ascends a hill, it works against the force of gravity. The engine must provide additional energy to overcome not only the usual resistance from friction and air drag but also the gravitational pull that is trying to pull the vehicle back down the hill. This additional resistance causes the vehicle to slow down unless greater power is applied.
Conversely, when a vehicle descends a hill, gravity accelerates the vehicle, adding to its motion. Therefore, less engine power is required to maintain speed, and even without any engine power, the vehicle will accelerate because of the gravitational force pulling it downhill. This is the same principle that would apply to the truck of mass 1.2 tons going down a 150 m hill mentioned in the question. The truck will convert its potential energy at the top of the hill into kinetic energy as it descends, potentially reaching its maximum velocity at the bottom depending on factors such as air resistance and mechanical efficiency.
However, the maximum velocity that the truck can achieve theoretically is when all its potential energy has been converted to kinetic energy. This is given by the formula KE = PE at the top of the hill where KE is kinetic energy and PE is potential energy. But in reality, the truck may not reach this speed due to energy losses such as air resistance, rolling resistance, and mechanical inefficiency. Friction also plays a role in determining the actual speed because it provides the necessary traction for the vehicle to move. Without it, the vehicle would not be able to climb uphill or safely navigate downhill, as friction allows control over the vehicle's speed.
The expression that suggests roads must be steeply banked for high speeds and sharp curves indicates that friction helps maintain control at varying speeds. The equation for the speed at the checkpoint provided, V = KVO, where K is a constant and V0 is the initial velocity of Car B, would not be correct if Car A starts from rest because V would always equal zero regardless of the value of K. This shows the importance of having a correct mathematical model when predicting velocities.