We begin with a lightning fast introduction to the basic tools of physics.

If you read chapter one of this book, you are now optimally prepared to learn physics. You are not afraid of numbers or simple algebra rules. You know how to solve equations. You are familiar with functions such as the linear function $f(x)=mx+b$ and the quadratic function $f(x)=ax^2+bx+c$. In particular you should know how to solve the quadratic equation. Sometimes there will be two unknowns to solve for in a physics problem, but this is not much harder. If you have two equations that you know to be true, then you can solve two equations simultaneously to find both unknowns.

Most of the cool quantities in physics are vectors $\vec{v}=(v_x,v_y)$. Velocity is a vector, forces are vectors, and the electric and magnetic fields are vectors too. Dealing with vectors involves dealing with their components. So saying that $\vec{a}=\vec{b}$ is really saying that the $x$ components of these vectors are equal \[ a_x = b_x, \] and their $y$ components are equal too: \[ a_y = b_y. \] So when I say that $\vec{v}_i = 0\hat{x} + 12\hat{y}$, I am saying that the $x$-component is zero $v_{ix} = 0$ and the $y$-component is twelve $v_{iy}= 12$. However, the teacher won't make physics easy for you on the homework, and definitely not on the exams. He or she won't tell you the vector components, but instead say something like “the initial velocity $\vec{v}_i$ is 12[m/s] and it acts at an angle of 90 degrees with respect to the $x$ axis.” This is the length-and-direction way of talking about vectors. To get the $x$ and $y$ components of the vector $\vec{v}_i$ you have to use cos and sin as follows: \[ v_{ix} = 12 \cos 90=0, \qquad v_{iy} = 12 \sin 90=12. \] If this doesn't seem obvious to you, then you should draw a right-angle triangle and recall the definitions of sin and cos.

We will discuss vectors in more depth in Chapter 3.

Yes, calculus. You need to understand calculus in order to understand mechanics properly. The two subjects are meant for each other. This is in fact the whole idea behind this book.

It is possible to teach physics without calculus. For example, a teacher could state the equations of kinematics (the area of physics which deals with the motion of objects) without proof. This “memorize the equations” approach is how physics is usually taught in high school. The equations are true “by revelation”. This is an OK way to learn physics when you are in high school, because the only mathematical technique you know as a kid is how to solve equations. Indeed just knowing how to use the equations of kinematics is quite enough to solve many physics problems.

Later on in this chapter (after learning a bit about calculus), we will revisit the equations of kinematics and see where they actually come from. You are adults now. You can handle the truth. Don't worry though, it won't take more than a couple of pages.