Respuesta :
Answer:
38.4 m/s
Explanation:
a) at t = 3.2s. [tex]x = 6 * 3.2^2 = 61.44 m[/tex]
b) at t = 3.2 + Δt. [tex]x = 6*(3.2 + \Delta t)^2[/tex]
c) As Δt approaches 0. We can find the velocity by the ratio of Δx/Δt
[tex]v = \frac{\Delta x}{\Delta t} = \frac{x_2 - x_1}{\Delta t}[/tex]
[tex]v = \frac{6*(3.2 + \Delta t)^2 - 61.44}{\Delta t}[/tex]
[tex]v = \frac{6(3.2^2 + 6.4\Delta t + \Delta t^2) - 61.44}{\Delta t}[/tex]
[tex]v = \frac{61.44 + 38.4\Delta t + \Delta t^2 - 61.44}{\Delta t}[/tex]
[tex]v = \frac{\Delta t(38.4 + \Delta t)}{\Delta t}[/tex]
[tex] v = 38.4 + \Delta t[/tex]
As Δt approaches 0, v = 38.4 + 0 = 38.4 m/s
a. The position of box at t = 3.20s is 61.44 meters
b.  The position at t = 3.20+ Δt is,  [tex]x(3.20+ \Delta t)=6*(3.20+ \Delta t)^{2}[/tex]
c. The velocity is 38.4 meter per second.
The position of box is given by as a function shown below,
           [tex]x(t)=6t^{2}[/tex]
where x is in meters and t is in seconds.
a. The position of box at t = 3.20s is,
       [tex]x(3.2)=6*(3.2)^{2}\\ \\x(3.2)=61.44m[/tex]
b. The position at t = 3.20+ Δt,
       [tex]x(3.20+ \Delta t)=6*(3.20+ \Delta t)^{2}[/tex]
c. Â We have to find
             [tex]\frac{\Delta x}{\Delta t}=\frac{x(3.20+\Delta t)-x(3.2)}{\Delta t}\\\\\frac{\Delta x}{\Delta t}=\frac{6[(3.2)^{2}+(\Delta t)^{2}+6.4\Delta t - (3.2)^{2} ]}{\Delta t} \\\\\frac{\Delta x}{\Delta t}=6 \Delta t +38.4[/tex]
When [tex]\Delta t[/tex] approaches to zero.
 Velocity =   [tex]\frac{\Delta x}{\Delta t}=38.4 m/s[/tex]
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