Question

(will give medal)
acceleration is defined as the rate of change for which of the following?
A. time
B. velocity
C. position
Displacement

Answer 1

acceleration is the slope (the derivative) of the velocity

Answer 2

and slope is the same thing as rate of change --- just in case you didn't know.

Answer 3

ok so can you elaborate on that a little more plz?

Answer 4

lets define:
displacement as \(\large\color{black}{ \displaystyle s(t) }\)
velocity as \(\large\color{black}{ \displaystyle s'(t) }\) \(\large\color{black}{ \displaystyle (}\) or v(t) \(\large\color{black}{ \displaystyle )}\)
acceleration as \(\large\color{black}{ \displaystyle s''(t) }\) \(\large\color{black}{ \displaystyle (}\) or a(t) \(\large\color{black}{ \displaystyle )}\)

Time is just what the x-scale.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Answer 5

velocity is the slope of the displacement
acceleration is the slope of velocity
acceleration is slope-of-slope of displacement

Answer 6

\(\large\color{black}{ \displaystyle s'(t) }\) is the notation for the 1st derivative, or the first time slope of \(\large\color{black}{ \displaystyle s(t) }\).
\(\large\color{black}{ \displaystyle s''(t) }\) is the notation for the 2st derivative, or the second time slope of \(\large\color{black}{ \displaystyle s(t) }\).

Answer 7

so the answer is velocity?

Answer 8

Yes

Answer 9

thanks :) giving you a medal

Answer 10

or inversely, \(\large\color{slate}{\displaystyle\int\limits_{~}^{~}a(t)~dt~=v(t)}\)

Answer 11

I don;t need a medal, but if you want you can