Respuesta :
Answer:
Instantaneous velocity is [tex]v=63[/tex] at t=1.
Explanation:
The height in feet after t second is given by y(t)=95t−16t2.
Average velocity is defined by:
[tex]v_{ave}=\frac{x_{f} - x_{i} }{t_{f} - t_{i} }[/tex].
i)
[tex]t_{i}=1\\x_{i}=y(1)=79\\t_{f}=1+0.1\\x_{f}=y(1+0.1)=85.14\\[/tex]
⇒ [tex]v_{ave}=61.4[/tex].
ii)
[tex]t_{i}=1\\x_{i}=y(1)=79\\t_{f}=1+0.01\\x_{f}=y(1+0.01)=79.6284\\[/tex]
⇒ [tex]v_{ave}=62.84[/tex].
iii)
[tex]t_{i}=1\\x_{i}=y(1)=79\\t_{f}=1+0.001\\x_{f}=y(1+0.001)=79.062984\\[/tex]
⇒ [tex]v_{ave}=62.98[/tex].
Instantaneos velocity is defined by: [tex]v=\lim_{\triangle t \to 0} \frac{\triangle x}{\triangle t}[/tex]
So we have seen "manually" that when [tex]\triangle t \rightarrow 0[/tex], [tex]v \rightarrow 63[/tex].
So instantaneous velocity must be [tex]v=63[/tex] at t=1.
