Instantaneous Velocity
Key Questions

Answer:
Instantaneous velocity is the derivative or slope of the distance function.
Explanation:
Let the distance function be
#s(x)# Then, the instantaneous velocity at x:
instantaneous velocity
#=v(x)=# #""_(hrarr0)^lim[s(x+h)s(x)]/h# hope that helps

Answer:
See explanation
Explanation:
If I remember correctly!!!
For this expression to be used you are talking about obtaining the velocity at any absolutely minute moment in time on a changing velocity.
The change in velocity is acceleration. The thing is; acceleration could also be changing giving you a double whammy!
If you were to plot the changing velocity against time then you would get a curve. The tangent to this curve at any point is the resulting acceleration.
Check this to make sure it is correct: the instantaneous velocity is a lead up to the process of differentiation and or integration in Calculus.

The instantaneous velocity is found by taking the derivative of the curve and then substituting in a value of x.
Example:
#f(x)=x^3# #f'(x)=3x^2# Below are the instantaneous velocities at various values of
#x# for the curve.#x=3 > f'(3)=3(3)^2=27# #x=0 > f'(0)=3(0)^2=0# #x=1 > f'(1)=3(1)^2=3# #x=5 > f'(5)=3(5)^2=75#