about to let a stone drop. What will happen? The advantage of a thought
experiment is that we do not actually have to be there in person. We can also do
impossible things like stopping the stone in mid-air or watching it in slow motion
over a short time interval.
According to Newton’s theory of gravity, the stone will fall. Nothing surprising
in that; the stone is attracted to the earth and will fall faster and faster as the
hand on our stopwatch ticks on. Another advantage of a thought experiment is
that we can ignore complicating factors like air resistance.
What is the stone’s speed at a given instant of time, say when the stopwatch
reads exactly 3 seconds after it has been released? How can we work this out?
We can certainly measure average speed but our problem is to measure
instantaneous speed. As it’s a thought experiment, why don’t we stop the stone
in midair and then let it move down a short distance by taking a fraction of a
second more? If we divide this extra distance by the extra time we will have the
average speed over the short time interval. By taking smaller and smaller time
intervals the average speed will be closer and closer to the instantaneous speed
at the place where we stopped the stone. This limiting process is the basic idea
behind Calculus.