I at first thought that (Sorry, I'm poor at math) all you had to execute was take your initial velocity, then add whatever friend were increasing it by as many times as you had actually units the t. This is not the case, and I understand the over formula offers the correct answers, I just don't understand why. As a curious human being who wants to be far better at physics and math, discovering why is important. F=ma i get, I deserve to handle equations because that delta v, orbit dynamics but this just has me for a loss.
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tl;dr Please define the equation to who who's smart however not mathematics smart.
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· 9y · edited 9y
Quantum ar Theory | mathematics Physics
This is an explanation that just uses an easy arithmetic, so i hope that will work-related for you. Girlfriend don't need calculus to acquire this formula; you just need to think a little bit around what velocity and acceleration mean. This won't be short, yet I expect it will be clear for someone that identifies as not terribly comfortable through math.
To start with, the formula you cite only works for consistent acceleration, so that is the only case we have to consider.
Let's consider first what happens if we have no acceleration, and something is just traveling in ~ velocity u the whole time the traveling. Climate the distance traveled in time t would be ut. (Example: your velocity is 30 mph and also you travel for 4 hours, so you travel 30mph*4hours = 120 miles.)
Now let's take into consideration the instance of constant acceleration. For example, let's imagine the you rise your velocity in ~ a continuous rate from 30 mph come 210 mph end the course of 4 hours; how far do you take trip in those 4 hours? You know it's an ext than 30mph*4 hrs (how much you'd gain if you invested the whole time in ~ your beginning and slowest velocity) but less than 210 mph* 4 hours (how far you'd gain if you invested the totality time at your final and also fastest velocity).
The key is to think about what your average velocity is. Because you are enhancing your velocity in ~ a stable rate, your average velocity is the mean of her initial and also final velocities 30 mph and also 210 mph, i.e., (30 mph + 210 mph)/2 = 120 mph. Therefore how far you travel is 120 mph* 4 hours = 480 miles, i.e., your median velocity time your travel time.
What would this look choose in general? Let's mean your starting velocity is u and your last velocity is w. Then your median velocity is (u+w)/2, so how much you take trip is (u+w)t/2.
Now here's the key: just how are w and also u related? Answer: This is whereby the acceleration a comes in. Acceleration is a measure up of the rate at which velocity changes; therefore if you rise your velocity by 180 mph in 4 hours, her acceleration is (180 mph)/4 hrs = 45 mph every hour.
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In general, then the acceleration a = (w-u)/t
Now let's put it all together. Plugging w=u+at into the expression for typical velocity gives:
(u+w)/2 = (u+u+at)/2 = (2u+at)/2 = u + (1/2)at
This is the median velocity. However we know what to carry out to obtain the displacement: multiply this by the time elapsed! for this reason the displacement is