We need to find the average velocity at each time interval.
The average velocity ΔV is the change in position at two moments divided by the change of time:
[tex]\begin{gathered} \Delta V=\frac{h_2-h_1}{t_2-t_1}=\frac{56t_2-0.83t_2^{2}-56t_1+0.83t_1^{2}}{t_2-t_1} \\ \\ \Delta V=\frac{56(t_2-t_1)-0.83(t^2_2-t^2_1)}{t_2-t_1} \end{gathered}[/tex]
Using the above formula for each interval, we find:
• [7,8]:
[tex]\Delta V=\frac{56(8-7)-0.83(8^{2}-7^{2})}{8-7}=56-0.83(15)=43.55[/tex]
• [7,7.5]:
[tex]\Delta V=\frac{56(7.5-7)-0.83(7.5^2-7^2)}{7.5-7}=\frac{56\mleft(0.5\mright)-0.83\mleft(7.25\mright)}{0.5}=43.965[/tex]
• [7,7.1]:
[tex]\Delta V=\frac{56(7.1-7)-0.83(7.1^2-7^2)}{7.1-7}=\frac{56(0.1)-0.83(1.41)}{0.1}\cong44.2970[/tex]
• [7,7.01]:
[tex]\Delta V=\frac{56(7.01-7)-0.83(7.01^2-7^2)}{7.01-7}=\frac{56(0.01)-0.83(0.1401)}{0.01}=44.3717[/tex]
• [7,7.001]:
[tex]\Delta V=\frac{56(7.001-7)-0.83(7.001^2-7^2)}{7.001-7}=\frac{56(0.001)-0.83(0.014001)}{0.001}\cong44.3792[/tex]
Therefore, the average velocities are:
[7,8]: 43.55 m/s
[7,7.5]: 43.965 m/s
[7,7.1]: 44.2970 m/s
[7,7.01]: 44.3717 m/s
[7,7.001]: 44.3792 m/s
