Need an idea for calculus presentation

[confused calc]

keep in mind that the people that i am presenting to have no clue what calculus is and i want to show them how they use it in everyday life.

 

[mathman]

Distance, speed, acceleration relationship could give examples. Free fall, car driving, plane travel are examples.

 

[fourier jr]

what about the 4 general problems that calculus was originally used for? that would be tangents to curves, problems of motion (especially planetary motion), arc lengths, areas & volumes under curves or bounded by curves, and maxima/minima problems.

 

[confused calc]

went with a demonstration using a football and how to use calculus to predict where the ball is going to go. in the end i think half the class was actually interested in calculus and the other half was a little overwhelmed.

 

[HallsofIvy]

Here's an example that I've used in introductory lectures: Imagine that you are in spaceship high above the plane of the solar system and you take a "snap shot" that includes both the sun and the planet Jupiter. Knowing the scale, you could use that snap shot to determine the distance from the sun to Jupiter at that instant. And, then, using Newton's gravity formula, you could calculate the force the sun exerts on Jupiter and so Jupiter's acceleration at that instant.

But what does "acceleration at a specific instant" mean? Acceleration is defined as "change in speed over change in time" and speed itself is defined as "change in distance over change in time". Both of those require a "change in time" and so make no sense "at a specific instant". That was the problem that Newton faced in developing his formula for gravitational force and he created Calculus to solve it!