Instantaneous velocity For the following position functions, make a table of average velocities similar to those in Exercise 1 and 2 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] |
|
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[2.9,3] |
|
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| [2.99, 3] |
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[2.999,3] |
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[2.9999, 3] |
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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] |
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[π/2, π/2 + 0.01] |
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[π/2, π/2 + 0.001] |
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[π/2, π/2 + 0.0001] |
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s(t) = 20/(t + 1) at t = 0
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