2006-09-05 17:03:21 · 3 answers · asked by ehsaant 1 in Education & Reference ➔ Homework Help
when they refer to constant rate of change that means that the derivative of the equation given is constant....
looking at your previous question posted, the constant rate of change would refer to a slope that is not changing. This is given by y=mx+b. m would be the constant rate of change.
there is no such thing as 'the' constant rate of change that can apply to every situation. In real world aplications, a constant rate of change would be the acceleration due to gravity. Acceleration of course would refer to the derivative of velocity with respect to time.... This quantity is neither decreasing or increasing therefore it is constant.
This can be proven as follows:
given that there is no air drag.... the equation for velocity is given by the derivative of Displacement with respect to time. That is:
dx/dt(x)=dx/dt(x0+v0t+-1/2gt^2)
dx/dt=v=v0-gt
Now that you have velocity, you take the derivative of it to get acceleration...
dx/dt(v)=dx/dt(v0-gt)
d^2x/dt^2=dv/dt=g...
since g is a constant, no matter what the given point in time, acceleration will always be the same. This, of course, is only when there is no air drag. If there were air drag then there would have to be a change in acceleration which is known as a jerk.
If you mean what is the average rate of change then this would mean the difference in y over the difference in x which is basically slope.... (the secent line of a curve).... the instantanous rate of change, however, refers to the slope of a curve at a given point known as the tangent line at that given point. This is, of course, the derivative of the function with respect to the x axis...
2006-09-05 17:06:55 · answer #1 · answered by venomfx 4 · 0⤊ 0⤋
Constant Rate Of Change
2016-10-31 10:52:24 · answer #2 · answered by mathison 4 · 0⤊ 0⤋
You mean CHANGE per se? No such thing as constant rate for that phenomenon. It could be progression or retrogression, coming in leaps and bounds, perpetual flux. The only thing constant about change is the fact that it changes.
2006-09-05 17:18:05 · answer #3 · answered by Bummerang 5 · 0⤊ 0⤋
Is 2,4,8,16 a pattern showing a constant rate of change?
2014-01-23 00:44:42 · answer #4 · answered by Jeanneane 1 · 0⤊ 0⤋
change per unit time is constant
like if constant change of velocity is 5m/s per second
then it is constant acceleration of 5m/s/s or 5m/s^2
2006-09-05 17:08:33 · answer #5 · answered by raj 7 · 0⤊ 0⤋