if y(x)=x^3+x^2+3
is it true that y(x)= the velocity. y'(x)= the accleration and y''(x)= the speed?
thanks
Where is this problem coming from? Typically in problems involving distance, speed, and accelertion y will be a function of time, not x.
Supposing we have y as a function of time, the usual definitions give y(t) as a displacement, y'(t) as a velocity, and y"(t) as an acceleration. This will not be the case for a function y(x) where x is a distance.
-Dan
As others have said, you cannot just pick out a function and ask if it is velocity. What a function represents depends upon the application.
Now, if y(t) is a position function, that is, if y(t) is interpreted as the position of some object at time t, the y'(t) is its velocity and y''(t) is its acceleration. The "speed" is just |y'(t)| the absolute value (or magnitude) of the velocity.