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for the function s(t)=-16t^2 + 104t, find the avg velocity at the time interval [1,1.01]

Sagot :

BrotherGoku

Answer:

71.8

Step-by-step explanation:

So the function s(t) describes  the displament of the object over a certain time. To find velocity, first you have to know what it is. Knowing that velocity is given by the unit m/s, which is distance over time, the slope of the s(t) under a certain time interval will be your velocity since it covers a certain distance over a time interval which is given [1,1.01].

So to find the slope, you do y2-y1 / x2 - x1. Therefore, you calculate the y value for each x then you apply the slope formula

x1 = 1

x2 = 1.01

y1 = -16(1)^2 + 104(1) = -16 + 104 = 88

y2 = -16(1.01)^2 + 104(1) = 88.718

88.718 - 88 / 1.01 - 1 = 0.718/0.01 = 71.8 s(t)/s

semsee45

Answer:

[tex]\overline{v}=71.84\; \sf m/s[/tex]

Step-by-step explanation:

To find the average velocity over the time interval [1, 1.01], we can use the formula for average velocity, which is the total displacement of an object divided by the total time taken for that displacement:

[tex]\overline{v}=\dfrac{s(t_2)-s(t_1)}{t_2-t_1}[/tex]

where:

  • v represents the average velocity.
  • s(t₁) and s(t₂) represent the positions of the object at times t₁ and t₂ respectively.
  • t₁ and t₂​ represent the starting and ending times of the interval over which the average velocity is being calculated.

In this case:

  • t₁ = 1
  • t₂ = 1.01

Substitute the values of t into the displacement function s(t) to calculate s(t₁) and s(t₂):

[tex]s(t_1)=-16(1)^2 + 104(1) \\\\ s(t_1)=-16 + 104\\\\ s(t_1)=88[/tex]

[tex]s(t_2)=-16(1.01)^2 + 104(1.01) \\\\ s(t_2)=-16(1.0201)+104(1.01)\\\\s(t_2)=-16.3216+105.04\\\\s(t_2)=88.7184[/tex]

Now, substitute the values into the average velocity equation:

[tex]\overline{v}=\dfrac{88.7184-88}{1.01-1} \\\\\\ \overline{v}=\dfrac{0.7184}{0.01} \\\\\\ \overline{v}=71.84[/tex]

Therefore, the average velocity at the time interval [1, 1.01] is 71.84 m/s, assuming that the distance is measured in meters and the time is measured in seconds.

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