How can we derive the distance formula using velocity and acceleration?

[david12]

Homework Statement

I try to drive distance formula which is S=vt+1/2at^2.



I use velocity and acceleration formula to drive the distance formula but i couldn't get the distance formula.is there anyone know how to drive S=vt+1/2at^2. and how that came from in the first place .

thank you.

 

[Kurdt]

Its the solution to the differential equation:

$$\frac{d^2s}{dt^2} = C$$

where c is a constant.

 

[Defennder]

A more graphical method involves drawing a velocity-time graph of an object under constant acceleration from velocity u to v. It should look like a trapezium whose parallel sides are parallel to the velocity axis. The area of the parallelogram gives you the displacement, and that is given by the formula.