# What is the speed of an object that travels from ( 7,-8,1)  to ( -1,4,-2 )  over 2 s?

Mar 20, 2018

Speed is distance over time.

We know the time.

The distance can be found via Pythagorean theorem:
$\Delta {s}^{2} = \Delta {x}^{2} + \Delta {y}^{2} + \Delta {z}^{2}$
$\Delta {s}^{2} = {\left(- 1 - 7\right)}^{2} + {\left(4 + 8\right)}^{2} + {\left(- 2 - 1\right)}^{2}$
$\Delta {s}^{2} = {8}^{2} + {12}^{2} + {3}^{2} = 64 + 144 + 9 = 217$
$\Delta s = \sqrt{217} \approx 14.73$

Therefore,
$v = \frac{s}{t} = \frac{14.73}{2} = 7.36$

A note on units: since the distance doesn't have units but the time does, technically the units for the speed would be inverse seconds, but that doesn't make any sense. I'm sure in the context of your class there will be some units that make sense.