Why is Reverse thrust more effective at higher airspeeds? It might seem logical at first but why is reverse thrust actually more effective at higher airspeeds?

If we assume that engine performance will not change during a 100 knot deceleration on landing roll-out, and engine is kept at constant reverse thrust throughout the whole landing then the engine will produce a constant force to slow the aircraft down. It won't be more effective at higher airspeeds because we are continuously redirecting a constant amount of air at specific velocity. Even if we include an engine performance change on landing roll-out, thrust will probably not change by more than a percent. Am I missing something?
From "handling The Big Jets" by D.P.Davies.

Reverse thrust is much more effective at high aircraft speeds than low speeds for two reasons. Firstly, the net amount of reverse thrust increases with speed because the acceleration imposed on the (constant) mass flow is greater. This is because the aircraft forward speed is additional when in reverse thrust as opposed to subtractional when in forward thrust. Secondly the power produced is higher at higher speeds because of the increased rate of doing work. In this context it means that the kinetic energy of the aeroplane is being destroyed at a higher rate at higher airspeeds.