Month: April 2023

This week’s post has something to do with Physics (position, velocity and acceleration) but it is mostly about good old plain Algebra and about reading the problem carefully. For starters, since this takes place here on Earth, the acceleration of an object due to gravity is \(\mathbf{-32}\) feet per second ...

Vectors are used all the time in Physics and I am still only learning how to use them. I will try to provide a good example of their usefulness. Suppose you spent a nice afternoon fishing and now you’re getting ready to go back home. A force of 600 pounds ...

One of the first things you learn when starting college-level Physics is vectors; right in the very first chapter. Vectors are also taught at some level in some Algebra and Trigonometry textbooks. That’s where I’ve reached to in order to get a more solid understanding of them. Let’s try this ...

I just came across a calculus word problem about integration; specifically, the area between two curves. Two runners, starting at the same location, run along a straight road for 1 hour. The velocity of one runner is \(\boldsymbol{v_1\left(t\right) = 7t}\) and the velocity of the other runner is \(\boldsymbol{v_2\left(t\right) = 10\sqrt{t}}\). ...

A few days ago was I wrote about Linear Approximations. These are used, as the name implies, to approximate the value of a function, usually a complicated function, by way of using a much simpler linear function, as long as \(\boldsymbol{\Delta x}\) (the change in x) is small. Along with ...

Smooth curves appear straighter on smaller scales and it is the basis of many important mathematical ideas, one of which is linear approximation. ...