Perhaps it will help if we derive the formula without using calculus.
This works only with uniform acceleration.
Fd = KE
F = ma
so, mad = KE
Draw a graph with time on the x axis and velocity on the y axis, then plot
a line at the origin with a slope equal to the acceleration of the body. This
tells you how fast the body is moving at a given moment of time. Now d is equal
to the area under the line for a given interval of time and it’s equal to vt/2.
Brilliant you can draw a graph and do away with calculus, if only it was that easy. The thing is calaculus is the graph, the line itself or the area below it’s line or sometimes above by extrapolating. You’re just doing what calculus does, really, really slowly and inefficiantly. Not to mention the fact you can much more easilly derive fundamentals like you give by using calculus. And in fact the reason why the fundamentals you give exist are because they were generally derived in all cases by using calculus, to do so by brute force is impossible. f=ma to give S=ut+1/2 at^2, you name it any change in any force is derived generally from first principles of calculus, it’s what Newton did. End of the day cart before the horse: you’re using the general solution derived by calculus to work out a solution that couldn’t exist without calculus and its general rules.
Have you ever tried working out complicated problems by only using just graphs though? Calculus does away with the graph because it presents a general case in all of x or y or z or variables given something dependant on the variables, it allows us to say any exact point on any graph will be a, something it takes a hell of a long time to do on a graph with limited scope. If you tried using just a graph to plot any sort of shape or line in any sort of problem that wasn’t simple you’d end up spending if not days, weeks, months, decades trying to figure the sums out. It’s a tool, of course you can use a graph that plots the value of area of square or a line between 1 and 10 or even 100, but can you plot the volume or line, exactly of a sphere or a circle, quickly, or of a complicated shape betweeen 1 and infinity? Calculus lets us do that if not instantly after a bit of time. Brute force well unless you are a topographical genius good luck to you.
