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For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t​ = 1.time interval [1,2][1,1.5][1,1.1][1,1.01][1,1.001]average velocity

Question

For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate average velocities. Then make a conjecture about the value of the instantaneous velocity at t​ = 1.

time interval  [1,2] [1,1.5] [1,1.1] [1,1.01] [1,1.001]
average velocity          
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Step 1

Consider the position function, s(t) = 16t2+103t.

s(b)-s(a)
Apply the average velocity formula over the interval [a, b] as v
to
b - a
complete the table as follows.
Compute the average velocity over the interval [1, 2] as follows.
s(2)-s(1)
2 1
16(2) +103(2)-16(1 -103 (1)
1
= 64 206-16 -103
- 151
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s(b)-s(a) Apply the average velocity formula over the interval [a, b] as v to b - a complete the table as follows. Compute the average velocity over the interval [1, 2] as follows. s(2)-s(1) 2 1 16(2) +103(2)-16(1 -103 (1) 1 = 64 206-16 -103 - 151

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Step 2

Compute the average velocity over the...

s(1.5)-s(1)
V
1.5
16(1.5) 103(1.5)16(1)-103(1)
0.5
36+154.5 16-103
0.5
=143
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s(1.5)-s(1) V 1.5 16(1.5) 103(1.5)16(1)-103(1) 0.5 36+154.5 16-103 0.5 =143

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