- #1

Feynstein100

- 162

- 16

The problem:

**An object is launched vertically upward with an initial velocity of 10 m/s from an elevation of 20m and allowed to hit the ground. Develop the equations of motion between elevation & velocity vs time. Also find the maximum elevation and maximum velocity attained by the object.**

The first part was too trivial to mention here. It was the second part that got me.

The maximum elevation was quite simple. I had an equation for elevation vs time. All I had to do was differentiate it and set it to zero. I noticed that this was intuitive because the derivative of elevation would be velocity and since this is projectile motion i.e. constant acceleration, its velocity at the highest point would be zero. And thus I was able to find the max elevation.

However, when it came to max velocity, I thought I could simply do the same thing again, since I had an equation for v vs t. But then I realized that if I differentiate that equation, I get acceleration, which is constant and not equal to zero.

This means I can't use the maxima/minima property of derivatives to find max velocity. Why didn't that work?

Okay I see now that the velocity increases linearly, meaning its graph on v vs t is a straight line. As such, its maxima and minima are at +

Is this only true for straight lines or are there other curves where the maxima-minima property doesn't work? Or at least, isn't useful