One of the coolest things about understanding math is that you will automatically start to understand the laws of physics too. Indeed, most physics laws are expressed as mathematical equations. If you know how to manipulate equations and you know how to solve for the unknowns in them, then you know half of physics already.
Ever since Newton figured out the whole $F=ma$ thing, people have used mechanics in order to achieve great technological feats like landing space ships on The Moon and recently even on Mars. You can be part of that too. Learning physics will give you the following superpowers:
It is possible to write down the equation which describes the position of
an object as a function of time $x(t)$ for most types of motion.
You can use this equation to predict the motion at all times $t$,
including the future.
"Yo G! Where's the particle going to be at when $t=1.3$[s]?",
you are asked. "It is going to be at $x(1.3)$[m] bro."
Simple as that. If you know the equation of motion $x(t)$,
which describes the position for //all// times $t$,
then you just have to plug $t=1.3$[s] into $x(t)$
to find where the object will be at that time.
- Special **physics vision** for seeing the world.
You will start to think in term of concepts like force, acceleration and velocity
and use these concepts to precisely describe all aspects of the motion of objects.
Without physics vision, when you throw a ball in the air you will see it go up,
reach the top, then fall down.
Not very exciting.
Now //with// physics vision,
you will see that at $t=0$[s] a ball is thrown into the $+\hat{y}$ direction
with an initial velocity of $\vec{v}_i=12\hat{y}$[m/s]. The ball reaches a maximum
height of $\max\{ y(t)\}= \frac{12^2}{2\times 9.81}=7.3$[m] at $t=12/9.81=1.22$[s],
and then falls back down to the ground after a total flight time of
$t_{f}=2\sqrt{\frac{2 \times 7.3}{9.81}}=2.44$[s].
A lot of knowledge buzz awaits you in learning about the concepts of physics and understanding how the concepts are connected. You will learn how to calculate the motion of objects, how to predict the outcomes of collisions, how to describe oscillations and many other things. Once you develop your physics skills, you will be able to use the equations of physics to derive one number (say the maximum height) from another number (say the initial velocity of the ball). Physics is a bit like playing LEGO with a bunch of cool scientific building blocks.
By learning how to solve equations and how to deal with complicated physics problems, you will develop your analytical skills. Later on, you can apply these skills to other areas of life; even if you do not go on to study science, the expertise you develop in solving physics problems will help you deal with complicated problems in general. Companies like to hire physicists even for positions unrelated to physics: they feel confident that if the candidate has managed to get through a physics degree then they can figure out all the business shit easily.
Perhaps the most important reason why you should learn physics is because it represents the golden standard for the scientific method. First of all, physics deals only with concrete things which can be measured. There are no feelings and zero subjectivity in physics. Physicists must derive mathematical models which accurately describe and predict the outcomes of experiments. Above all, we can test the validity of the physical models by running experiments and comparing the outcome predicted by the theory with what actually happens in the lab.
The key ingredient in scientific thinking is skepticism. The scientist has to convince his peers that his equation is true without a doubt. The peers shouldn't need to trust the scientist, but instead carry out their own tests to see if the equation accurately predicts what happens in the real world. For example, let's say that I claim that the equation of motion for the ball thrown up in the air with speed $12$[m/s] is given by $y_c(t)=\frac{1}{2}(-9.81)t^2 + 12t+0$. To test whether this equation is true, you can perform the throwing-the-ball-in-the-air experiment and record the maximum height the ball reaches and the total time of flight and compare them with those predicted by the claimed equation~$y_c(t)$. The maximum height that the ball will attain predicted by the claimed equation occurs at $t=1.22$ and is obtained by substituting this time into the equation of motion $\max_t\{ y_c(t)\}=y_{c}(1.22)=7.3$[m]. If this height matches what you measured in the real world, you can maybe start to trust my equation a little bit. You can also check whether the equation $y_c(t)$ correctly predicts the total time of flight which you measured to be $t=2.44$[s]. To do this you have to check whether $y_c(2.44) = 0$ as it should be when the ball hits the ground. If both predictions of the equation $y_c(t)$ match what happens in the lab, you can start to believe that the claimed equation of motion $y_c(t)$ really is a good model for the real world.
The scientific method depends on this interplay between experiment and theory. Theoreticians prove theorems and derive physics equations, while experimentalists test the validity of the equations. The equations that accurately predict the laws of nature are kept while inaccurate models are rejected.
The best of the equations of physics are collected and explained in textbooks. Physics textbooks contain only equations that have been extensively tested and are believed to be true. Good physics textbooks also show how the equations are derived from first principles. This is really important, because it is much easier to remember a few general principles at the foundation of physics rather than a long list of formulas. Understanding trumps memorization any day of the week.
In the next section we learn about the equations $x(t)$, $v(t)$ and $a(t)$ which describes the motion of objects. We will also illustrate how the position equation $x(t)=\frac{1}{2}at^2 + v_it+x_i$ can be derived using simple mathematical methods (calculus). Technically speaking, you are not required to know how to derive the equations of physics—you just have to know how to use them. However, learning a bit of theory is a really good deal: reading a few extra pages of theory will give you a deep understanding of, not one, not two, but eight equations of physics.