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:
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.
