What Zaphod seems to be saying in so many words is that, the closer you get to c, the more energy it takes to push a mass faster. And at c itself, the energy required for greater acceleration becomes infinite.

Therefore nothing with mass can reach or exceed the speed of light. Only something massless like photons can do that.

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...And that, my liege, is how we know the Earth to be banana-shaped. --Sir Bedevere