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F = ma. Power is not relevant. F means torque in the case of an engine.
Indeed, power is just torque x time and bhp is a derived figure. The horsepower curve is not measured but calculated. The torque curve is measured and converted into bhp (that's the origin of the b for brake)
It is a common misconception that power to weight ratio is a helpful number and comes from a time when horsepower was the only figure the engine manufacturer published.
Power is indeed the rate at which Work is done and Work is just not related to acceleration. Power is a constant speed factor and is a good indicator of top speed, but not acceleration.
With two vehicles compared and each has the correct gearing power to weight can be considered to be useful for comparing predictions about acceleration intervals but only as a stand in for torque. Look at the torque curves and the weights and you'll literally see the acceleration curve differences. This is especially true when comparing supercharged engines or diesel to gasoline for example.
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