Consider s(t)=5sin(t) describes a block bouncing on a spring. Complete the table with average velocities. Make the conjecture about the value of the instantaneous velocity at t=pi/2?
[ #pi/2# , #pi# ] [ #pi/2# , #pi/2# +0.1][ #pi/2# , #pi/2# +0.01]
[
1 Answer

#v_"av" = 3.18# #"m/s"# 
#v_"av" = 0.250# #"m/s"# 
#v_"av" = 0.0250# #"m/s"#
Explanation:
We're asked to calculate the average velocity for three different time intervals, and the instantaneous velocity at
1.
For the
Next, we'll use the average velocity formula
The quantity
(I'm assuming the distance units are meters.)
The quantity
The average velocity is thus
2.
Similarly, we'll plug in the times and find the position, then use this to find the average velocity:
3.
4.
As we can see, if we keep plugging in smaller time intervals, the average velocity gets closer and closer to