How is gravity a quadratic function?

1 Answer
Jul 13, 2015

Refer to explanation.

Explanation:

We can apply quadratic functions to objects that are in motion under gravity. For this explanation, we take a look at one of the equations of motion from physics that itself is a quadratic function and we set the acceleration of an object as being influenced by gravity.

Recall that a quadratic equation looks like the following:

f(x)=ax^2+bx+c

If we were to recall one of equations of motion from physics, such as the equation:

x_f-x_0=v_0*t+1/2a*t^2

where, x_f-x_0=change in position of x=Deltax

and if we consider our acceleration, a, to be the gravitational acceleration g, then

Deltax=v_0*t+1/2g*t^2

rearranging this equation gives

Deltax=1/2g*t^2+v_0*t

and making the change in the position of x with respect to time t gives

Deltax(t)=1/2g*t^2+v_0*t

the 1/2g part is like the a part in f(x)=ax^2+bx+c

the v_0 part is like the b part in f(x)=ax^2+bx+c

c is just some constant (some number), so think of c in the equation Deltax(t)=1/2a*t^2+v_0*t
as being equal to 0, (c=0)

the t's are like the x's in f(x)=ax^2+bx+c

So, if we look at them together:

f(x)=(a)x^2+(b)x+c

Deltax(t)=(1/2a)t^2+(v_0)t