meaning of the phrase "moment's thought"?

Question

Here it goes in context:

You should give your body a moment's thought.

It is understandable that it means to pay attention to something, but that sounds weird. Why is it not give something a moment of thought? Do those two phrases mean the same?

Answer 1

That sentence means

You should think for a moment about your body.

When we give something some thought, we think about it.

A moment's thought means "the thought of a moment", the thought that transpires in and for a moment.

Compare

He needed a day's rest.

A month's delay is unacceptable.

Each ring on the tree represents a year's growth.

They went to London for a fortnight's stay.

Answer 2

As an addon to Tromano's answer, a quote from a beautiful poem titled "What is life?" by John Clare:

And what is Life? An hour-glass on the run,
A mist retreating from the morning sun,
A busy, bustling, still-repeated dream.
Its length? A minute's pause, a moment's thought.
And Happiness? A bubble on the stream,
That in the act of seizing shrinks to nought.