Simply calculate the derivative? The velocity is indeed described by that, so:
If you plug in t = 1 your derivative will be 4 - 2 = 2. The unit of this derivative is meters / second since you derived position (in meters) to time (in seconds).
So the question is:
Suppose an object moves along a horizontal path with the position function x(t) = 4t – t^2 on the time interval 0 ≤ t ≤ 5, where x is measured in meters and t is measured in seconds. Find the instantaneous velocity of the object from t = 1. Use units to describe what this value means.
I know that the first step is to find the derivative of the position function so:
lim(delta x -> 0) [s(t + delta t) - s(t)] / [delta t]
[((4t + delta t) - t^2) - (4t - t^2)] / [delta t]
Now I don't understand how to simplify this so that I can plug in 1 for t?
I'm sorry if this looks confusing.
Any help is appreciated.
This is incorrect. What you want is
Multiply out and and cancel what you can. You should be able to cancel everything in the numerator that does NOT have a " " in it, factor out of the numerator and cancel with the .
Now I don't understand how to simplify this so that I can plug in 1 for t?
I'm sorry if this looks confusing.
Any help is appreciated.