物理問題(力學+光學)

You have mixed up with the symbols. The v in the formula P = F.v stands for the average velocity, and thus the power P so calculated is the average power.
[if the velocity v is the instantaneous velocity, then P becomes the instantaneous power].

In the calculation shown by you. Clearly, the object is under an acceleration. As such, the [v] now stands for the final velocity, but NOT the average velocity. The power calculated is thus the maximum power (power at the maximum final velocity)

In situation of a constant accelration, the average velocity v(av) equals to half of the final velocity v(f), if the object starts from rest (i.e. u = 0 m/s as in your case), hence, v(av) = v(f)/2

If multiply both sides by the force F (assume constant for a constant acceleration), thus the maximim power P(max) and avergae power P(av) are related by
P(av) = F.v(av) = F.[v(f)/2] = P(max)/2

Since P(av) = mv(f)^2/2t
hence, P(max) = 2.P(av) = mv(f)^2/t, which is exactly your result.
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There is no universal diagram.
In fact, there are only two "basic light rays".
(1) light ray parallel to the pricnicpal axis is refracted to pass through (or appear to pass through) the focus;
(2) light ray passes through the centre of the lens is undeviated.

Based on these two "basic light rays", you could draw any rays you want.



2009-12-03 14:51:10 補充：
Following your calculation, the correct one should be
P(av) = F.v(av) = ma.v(av) = m[v(f)/t].v(av) = m.[v(f)/t].[v(f)/2] = m.v(f)^2/2t =KE/t
see how you have mixed up the two velocities.

第一題你要用積分做的，就咁做已經係有問題