Expert: Paul Klarreich - 1/23/2006

Question
Hi Mr. Klarriech,
Recently I have been requested to teach calculus and its applications to older students   . I am currently doing Motion in a straigtht line where we diferenciate S(distance) formula to obtain velocity and then acceleration. The only real life situation that I can think of and see regularly in the questions pertaining to this chapter is when a stone is thrown vertically upwards. In this case there will be on turning point when the stone reaches the highest. Some questions provides 2 instances where the velocity is zero. Could you kindly tell me some real life situations where motion in a straight line is really meant especially when there are 2 moments when the speed is zero?

Regards
roy

Answer
Hi, Roy

Your question:

Recently I have been requested to teach calculus and its applications to older students . I am currently doing Motion in a straight line where we differentiate S(distance) formula to obtain velocity and then acceleration. The only real life situation that I can think of and see regularly in the questions pertaining to this chapter is when a stone is thrown vertically upwards. In this case there will be on turning point when the stone reaches the highest. Some questions provides 2 instances where the velocity is zero. Could you kindly tell me some real life situations where motion in a straight line is really meant especially when there are 2 moments when the speed is zero?
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Yes, that is the most common application.  Others are generally either rather contrived or complicated.  But you might try something like this:

A weight is hanging from a metal spring.  (Sort of like a car resting ON its springs.)  When the weight is pulled down, away from its equilibrium point, and then released, the weight oscillates up and down.  (You could change this to right and left.)

This is because the spring pulls back on the weight causing it to move upward.  But the weight moves past the E.P. compressing the spring which now PUSHES back on the weight, slowing it and eventually causing it to move downward, etc.

The equation of motion is

h = h0 cos kt, where

h is the displacement away from the E.P.
h0 is the initial displacement ...
k is the natural frequency.

Now you can start asking questions about it.  You could try some kind of 'pendulum' application, too.

I'm sorry no other obvious situations come to mind.

Paul