Given that the mass is m = 82 kg.
For pushups,
The initial velocity is u = 0 m/s
The distance is 26 cm = 0.26 m
The time is
[tex]\begin{gathered} t=\frac{14.64}{10} \\ =1.464\text{ s} \end{gathered}[/tex]First, we have to find final velocity,
[tex]\begin{gathered} v=\frac{d}{t} \\ =\frac{0.26}{1.464} \\ =0.177\text{ m/s} \end{gathered}[/tex]The acceleration can be calculated as
[tex]\begin{gathered} a=\frac{v-u}{t} \\ =\frac{0.177-0}{1.464} \\ =0.12m/s^2 \end{gathered}[/tex]The force will be
[tex]\begin{gathered} F=ma \\ =82\times0.12 \\ =9.84\text{ N} \end{gathered}[/tex]The number of reps = 10
The work done will be
[tex]\begin{gathered} W=\text{Force}\times dis\tan ce \\ =9.84\times0.26\text{ m} \\ =2.5584\text{ J} \end{gathered}[/tex]This is for one repetition.
For 10 repetitions the work will be
[tex]\begin{gathered} W_{10}=2.5584\times10 \\ =25.584\text{ J} \end{gathered}[/tex]The time taken for 10 repetitions will be 14.64 s.
The power will be
[tex]\begin{gathered} P=\frac{W_{10}}{t} \\ =\text{ }\frac{\text{25.584}}{14.64} \\ =1.747\text{ W} \end{gathered}[/tex]For staircase,
Distance, d = 146 cm = 1.46 m
The time will be
[tex]\begin{gathered} t\text{ = }\frac{2.39+(9\times2.05)}{10} \\ =2.084\text{ s} \end{gathered}[/tex]The initial velocity is u = 0 m/s
The final velocity is
[tex]\begin{gathered} v=\frac{d}{t} \\ =\frac{1.46}{2.084\text{ }} \\ =0.700\text{ m/s} \end{gathered}[/tex]The acceleration will be
[tex]\begin{gathered} a=\frac{0.7-0}{2.084} \\ =0.335m/s^2 \end{gathered}[/tex]The force will be
[tex]\begin{gathered} F=\text{ ma} \\ =82\times0.335 \\ =27.47\text{ N} \end{gathered}[/tex]The number of repetitions = 10
The work will be
[tex]\begin{gathered} W=F\times d \\ =27.47\times1.46 \\ =40.106\text{ J} \end{gathered}[/tex]For 10 repetitions, the work done will be
[tex]\begin{gathered} W=10\times40.106 \\ =401.06\text{ J} \end{gathered}[/tex]The time will be
[tex]t=\text{ 20.84 s}[/tex]The power will be
[tex]\begin{gathered} P=\frac{W_{10}}{t} \\ =\frac{401.06}{20.84} \\ =19.24\text{ W} \end{gathered}[/tex]For squats,
The distance will be d = 21 cm = 0.21 m
The time will be
[tex]\begin{gathered} t=\frac{14.43}{10} \\ =1.443\text{ s} \end{gathered}[/tex]The initial velocity is u = 0 m/s
The final velocity will be
[tex]\begin{gathered} v=\frac{d}{t} \\ =\frac{0.21}{1.443} \\ =0.145\text{ m/s} \end{gathered}[/tex]The acceleration will be
[tex]\begin{gathered} a=\frac{v-u}{t} \\ =\frac{0.145-0}{1.443} \\ =0.1004m/s^2 \end{gathered}[/tex]The force will be
[tex]\begin{gathered} F=ma \\ =82\times0.1004 \\ =8.23\text{ N} \end{gathered}[/tex]The number of repetitions will be 10.
The work done will be
[tex]\begin{gathered} W=F\times d \\ =8.23\times0.21 \\ =1.73\text{ J} \end{gathered}[/tex]The work done for 10 repetitions will be
[tex]\begin{gathered} W_{10}=1.73\times10 \\ =17.3\text{ J} \end{gathered}[/tex]The time taken will be 14.43 s.
The power will be
[tex]\begin{gathered} P=\frac{W_{10}}{t} \\ =\frac{17.3}{14.43} \\ =1.19\text{ W} \end{gathered}[/tex]
