Answer:
The skate boarder travels 162.2413 meters
Explanation:
Notice that the skateboarder is traveling with with a stopping motion (negative acceleration since the velocity is reducing until it gets to zero - stopped final situation).
We can use the equation that relates velocity (v) with acceleration ([tex]a[/tex]), to find the value of such negative acceleration:
[tex]change\,\,in\,\,velocity= a * t\\v_f-v_i=a* t[/tex]
where the subindeces for the velocity (v) correspond to final and initial states.
In our case, the final velocity is zero (stopped), the initial velocity is 33.7 m/s, and the elapsed time is 9.62 seconds, therefore we can use this equation to find the acceleration "[tex]a[/tex]":
[tex]v_f-v_i=a* t\\(0-33.7)\,\frac{m}{s} =a\,(9.62\,\,s)\\a=\frac{-33.7}{9.62} \,\frac{m}{s^2}\\a=-3.50\,\,\frac{m}{s^2}[/tex]
Now that we know the acceleration, we can estimate the distance covered in that time, using the position equation:
[tex]Change\,\,in\,\,Position=v_i\,t+\frac{1}{2} a\,t^2\\Change\,\,in\,\,Position=33.7\,(9.62)\,+\frac{1}{2} (-3.50)\,9.62^2\\Change\,\,in\,\,Position=162.2413\,\,m[/tex]
