Hydroelectric power plants convert the gravitational potential energy of falling water into electrical power, typically by allowing the water to flow through a pipe called a penstock to rotate a generator located below it. let the bottom of the penstock be the origin of a cartesian coordinate system and the point at which the gravitational potential energy is zero.

Many machines- including inclined planes such as ramps- increase the strength of the force put into the machine but decrease the distance over which the force is applied.

What is the speed of an object at a given moment?

Amachinist turns the power on to a grinding wheel, at rest, at time t = 0 s. the wheel accelerates uniformly for 10 s and reaches the operating angular velocity of 96 rad/s. the wheel is run at that angular velocity for 40 s and then power is shut off. the wheel slows down uniformly at 1.5 rad/s2 until the wheel stops. in this situation, the time interval of deceleration is closest to: