compute the average velocity of a stone over time intervals
1, 1.01
1, 1.001
1, 1.0001
and
.99,1
.999,1
.9999,1.
use this to estimate instantaneous velocity at t=1
All i can figure out the formula should be s(t1)-s(t0) over t1-t0
how does that give you a number what am i missing
Without the definition of S(t), we are not able to do the required calculations.
To compute the average velocity of a stone over a time interval, you can use the formula: average velocity = (change in position) / (change in time). In this case, the change in position is given as the difference between the final and initial positions of the stone, and the change in time is the difference between the final and initial time values.
For example, let's consider the first time interval 1 to 1.01. The initial position (s0) is given as 1 and the final position (s1) is also given as 1.01. Similarly, the initial time (t0) is 1 and the final time (t1) is 1.01.
Now, you can substitute these values into the formula:
Average velocity = (s1 - s0) / (t1 - t0)
= (1.01 - 1) / (1.01 - 1)
= 0.01 / 0.01
= 1 unit/time
Similarly, you can compute the average velocity for the other time intervals. The average velocity will be constant if the stone is moving at a constant speed.
To estimate the instantaneous velocity at t = 1, you need to take the average velocity of smaller and smaller time intervals around t = 1. In other words, you can consider the average velocities for the time intervals that are increasingly closer to t = 1, such as 0.99 to 1, 0.999 to 1, 0.9999 to 1, and so on. As the time intervals become infinitesimally small, the average velocity becomes an approximation of the instantaneous velocity at t = 1.
Finally, you can take the average of these estimated instantaneous velocities to obtain a more accurate estimation of the instantaneous velocity at t = 1.