Instantaneous velocity For the following position functions, make a table of average velocities similar to those in Exercise and make a conjecture about the instantaneous velocity at the indicated time.
Exercise 1
Instantaneous velocity Consider the position function s(t) = −16t2 + 100t. Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = 3.
Time interval | Average velocity |
| ||
[2,3] |
|
| ||
[2.9,3] |
|
| ||
| [2.99, 3] |
| ||
[2.999,3] |
|
| ||
[2.9999, 3] |
|
|
Exercise 2
Instantaneous velocity Consider the position function s(t) = 3 sin f that describes a block bouncing vertically on a spring. Complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t = −π/2.
Time interval | Average velocity |
[π/2, π] |
|
[π/2, π/2 + 0.1] |
|
[π/2, π/2 + 0.01] |
|
[π/2, π/2 + 0.001] |
|
[π/2, π/2 + 0.0001] |
|
s(t) = −16t2 + 80t + 60 at t = 3
We need at least 10 more requests to produce the solution.
0 / 10 have requested this problem solution
The more requests, the faster the answer.