TRANSPORTATION ENGINES: The internal combustion engines of automoblies trucks create a force that is applied to the roadway at their areas of contact with the roadway. The work associated with vehicle motion is only the work required to overcome wind drag. Vehicle motion does not include workat thre power truck engines supply for their motion varies considerably through the gears, speeds and such.
To avoid that detail, this discussion will address "average" forces of acceleration and braking.
Acceleration: In normal usage a truck loaded to 80,000 pounds would move horizontally from stop to a speed of 40 miles per hour (27 feet per second) in about 1/4 mile (1320 feet). What average horsepower is required of the engine to accomplish this speed?
This is aan increment type event. The energy equation is:

Potential energies are negligible and the work of the event can be expressed as an integral:

The mean value theorem of calculus is used to reduce the integral.

Next, numbers are applied and we see the time of the event must be determined.

If acceleration is constant then velocity increases linearly from zero to 27 feet per second. Therefore the avreage velocity would be one half the final velocity and the distance travelled would equal the average velocity times the time.

With the time, we return to the energy equation.
