A 2.0-kg weight plate is moving on a rough, horizontal surface where the coefficient of kinetic friction is 0.100. It is moving at 5.00 m/s until friction causes it to stop. Calculate the average power generated by friction on the plate as it comes to a stop.

Drag force from the air is the dominant resistive force acting on a motorcycle moving at constant speed on a flat surface (other forms of friction can be ignored). The work done by the engine is dissipated as work is done against drag force. We'll treat the motorcycle with the rider as having a cross-sectional area of 0.65 m² and a drag coefficient of 0.75. We'll also take the density of air to be 1.2 kg/m³. The motorcycle's engine generates power by burning gasoline. Taking the energy value of gasoline as 45 MJ/kg and the engine/transmission to be 28% efficient at converting chemical energy in gasoline to mechanical energy, find the engine's rate of consuming gasoline (in watts) when driving at a constant speed of 40 km/h.

Air exerts a significant drag force on moving objects. A motorcycle rider needs to keep the engine on when riding at constant speed on a flat surface to counter drag effects. Presume that all the engine's mechanical energy output is converted to work against drag, the rider/motorcycle has a cross-sectional area of 0.80 m², and a drag coefficient of 0.85 due to aerodynamic inefficiency. Take the density of air to be a typical 1.2 kg/m³ and the engine/transmission to be 31% efficient at converting chemical energy to mechanical energy. Determine the chemical energy intake of the engine in kCal ( 1 kCal = 4.19 kJ) when a rider travels at 50 km/h for 40 minutes. 

Suppose there's a system where water is pumped to a rooftop tank 80 m above ground level. The water is pumped at a steady rate of 1.2$\times$10⁵ kg/s for 12 hours. Calculate the total energy consumption, in kWh, needed to pump water to the rooftop tank.

In a facility for water storage, a tank holds water at an elevation of 150 m above ground level. Water is continuously pumped into the tank at a rate of 8000 kg/s for 12 hours. Assuming all the stored energy is discharged over 16 hours with an efficiency of 80%, what is the average power output during the release phase?

An electric car with a mass of $1,500$ kg is moving along a straight road. The car's position (in meters) as a function of time is given by the equation x(t) = 3t³ - 15t² + 24t, where t is in seconds. Calculate the average net power delivered to the car's wheels during the intervals from t = 0 s to t = 3.0 s, and from t = 3.0 s to t = 6.0 s.

A storage tank is located on top of a roof of a 95-meter-tall building. This storage tank contains a liquid. Through smooth pipes, the liquid is able to flow vertically down into a generator which produces electricity by using the mechanical energy of the liquid. Given that the efficiency of the generator is 44% and the rate at which the liquid flows down is 32 kg/s, evaluate what the rate of transfer of mechanical energy from the liquid to the generator will be.