I understand that if the velocity is constant (acceleration=$0$) throughout the course of motion (where graph shows a rectangle) then it would simply be like playing with equation:
(1). velocity=displacement/time
(2). displacement=velocity $\times$ time
=area of rectangle
=Velocity-axis $\times$ time-axis,
putting the value of velocity and time, then getting out the displacement.
But what if the acceleration is constant instead of $0$ (where graph shows a triangle) ? I know it would be $\frac{1}{2}$ velocity $\times$ time, but how we can put a value of velocity in
(1) displacement=velocity $\times$ time
When velocity is changing all time due to uniformly accelerated motion?
Best Answer
Imagine dividing your graph of velocity vs. time into a bunch of extremely thin vertical rectangles. It's reasonable to say that, over such a short time, velocity is constant in any given rectangle. So we can say that the distance traveled in each tiny instant of time is equal to the velocity in that interval times the length of the interval (i.e. the area of the rectangle). Add up the distance traveled over each thin rectangle and you get the total distance traveled.