Horsepower Torque Acceleration
This is an intuitive or logical look at horsepower, torque, and acceleration.
Torque is nothing but twisting force, or pressure. People comfortable with electricity would closely relate torque to voltage. Torque is an ability to move things, but by itself torque doesn't tell us something moved or can move. Torque is just pressure.
An example might be a person's ability to generate torque. If we pull the engine and put a long breaker bar on the transmission, a strong heavy person might be able to put four hundred pound-feet on a three foot lever. That isn't going to generate much speed or accelerate a heavy vehicle much. A strong person, with some training, might be able to throw a baseball 90 MPH, but he would lack the horsepower to move heavier or less aerodynamic items anywhere near that fast.
A human, using a series of levers, pulleys, or gears, might be able to move 10,000 pounds. But a single human could not rapidly move so much weight. A single human might be able to make something move 100 miles an hour, but not for any distance and certainly not with any weight or resistance to movement.
If we twist or push on some object and the rate of speed is zero, there isn't anything except static pressure. Without movement over time, power is zero, acceleration is zero.
The world had pressure and distance, the world had pressure and time. The world lacked a simple clear way to put distance, time, and force together to define ability to do a certain amount of actual work.
In the 1700's, Scotsman James Watt invented the steam engine. Watt was trying to sell steam engines as a replacement for horses or water wheels used at mills and mines.
There wasn't a simple, intuitive, way to explain the work capacity of the steam engine to others. The world had torque or force, people readily understood weight and pressure, but the world lacked a clear universal concept describing a machine's work capacity. The only intuitive explanations were how many horses or what size water wheel or wind blades it might take to run a machine, turn a mill stone, or move plows, wagons, or coaches. Farmers knew how many horses they needed to plow their field, and Wells Fargo had an idea how many horses it took to pull a stage coach a certain speed over a certain route. The industrialized, farming, and transportation world intuitively understood horses and a horse's ability to move weight at a certain rate, time, and distance.
Watt analyzed horse-powered mechanical systems in his intended engine market. Watt used the work generated in those systems to define the power of his steam engines. For obvious reason, Watt called the new measurement "horsepower". Horsepower painted a mental picture of how many "horses" a machine could replace.
Watt did this by using torque (or force) and distance in a certain time. All three things had to exist in the definition of work. Watt defined one horsepower as 32,572 feet distance * 1 foot-pound per minute. A typical horse moving a mill stone could move something 32,573 feet with one foot-pound of torque in one minute. The formula was rounded to 33,000 feet distance * (lb-ft torque / 1 minute time), or 33,000 foot pounds per minute / 2π radians per revolution, which simplifies to Torque * RPM / 5252
Watt's defining of power, or the ability to do work, even carried over to electricity. In honor of Watt, the standard measurement of electrical power became the watt. A watt is defined by two vectors, voltage (the across vector) and current (the through vector). One volt across with one ampere flowing through is defined as one watt. E times I = W. 746 watts or 33,000 BTU/h is approximately one horsepower.
The simplification of all of this is that horsepower is what moves our cars and determines ET and speed capacity for a given weight, and we can express horsepower in watts or horsepower, and even as boiler heat.
Acceleration (the actual work)
The ability to accelerate or move an object any distance is not described by torque. Ignoring system losses or inefficiencies, the ability to accelerate or generate speed is defined by horsepower, weight, and time. It all eventually translates down to Newton's third law, the tires push against the road and the road equally pushes back against the tire.