To calculate the other physical quantities in kinematics, we must introduce the time variable. The time variable allows us not only to state the position of the object during its motion, but also how fast it is moving. The speed at which an object is moving is given by the rate at which the position changes with time. For each position xi, we assign a particular time ti. If the details of the motion at each instant are not important, the rate is usually expressed as the average velocity. This...

A heat engine is a device used to extract heat from a source and then convert it into mechanical work used for various applications. For example, a steam engine on an old-style train can produce the work needed for driving the train.
Whenever we consider heat engines (and associated devices such as refrigerators and heat pumps), we do not use the standard sign convention for heat and work. For convenience, we assume that the symbols Qh, Qc, and W represent only the amounts of heat transferred...

The internal combustion engine is a heat engine that uses the byproducts of combustion as the working fluid instead of using a heat transfer medium to transfer heat. The combustion is done in a way that produces high-pressure combustion products that can be expanded through a turbine or piston to create work. Internal combustion engines can again be categorized into three kinds: (1) spark ignition gasoline engines, most commonly used in automobiles, (2) compression ignition diesel engines that...

An Otto engine is a four-stroke engine that uses a mixture of gasoline and air as the working fuel. The fuel is injected into the cylinder, and the piston is moved completely down so that the cylinder is at maximum volume. By moving the piston up, adiabatic compression takes place. The spark plug ignites the gasoline-air mixture, and the burning fuel adds heat to the system at a constant volume. The heated mixture expands adiabatically and gets further cooled by exhausting heat, and this cyclic...

Free jets describe the flow of liquid exiting a reservoir through an opening into the atmosphere without resistance. The velocity (v) of the liquid jet is derived using Bernoulli's principle and expressed as:

Understanding how an object moves along a path requires distinguishing between motion over a time span and motion at a precise moment. A useful example is a vehicle traveling along a straight and level path, where its position at any given time is known. The initial step in analyzing this motion is to measure how far the vehicle travels over a fixed time period. This measurement, called average velocity, is computed by dividing the total change in position by the duration over which the change...