Question

A skateboarder starts at 33.7 m/s and comes to a stop in 9.62 s. How far does it get?

Answer 1

Answer:

324.194 m

Explanation:

distance = speed × time

Answer 2

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 ($a$), to find the value of such negative acceleration:

$change\,\,in\,\,velocity= a * t\\v_f-v_i=a* t$

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 "$a$":

$v_f-v_i=a* t\\(0-33.7)\,\frac{m}{s} =a\,(9.62\,\,s)\\a=\frac{-33.7}{9.62} \,\frac{m}{s^2}\\a=-3.50\,\,\frac{m}{s^2}$

Now that we know the acceleration, we can estimate the distance covered in that time, using the position equation:

$Change\,\,in\,\,Position=v_i\,t+\frac{1}{2} a\,t^2\\Change\,\,in\,\,Position=33.7\,(9.62)\,+\frac{1}{2} (-3.50)\,9.62^2\\Change\,\,in\,\,Position=162.2413\,\,m$