What is the speed of an object that travels from #( 4,-2,2) # to #( -3, 8,-7 ) # over #2 s#?

Question

What is the speed of an object that travels from #( 4,-2,2) # to #(  -3, 8,-7 )   # over #2 s#?

Julia Aguilar · Accepted Answer

The speed of the object is traveling at 7.5825 (unknown) distance units per second.

Warning! This is only a partial solution, since distance units were not indicated in the problem statement. The definition of speed is #s=d/t# where #s# is speed, #d# is the distance the object travels over a span of time, #t#. We want to solve for #s#. We’re given #t#. We can calculate #d#. In this case, #d# is the distance between two points in a 3-dimensional space, (4, -2, 2) and (-3, 8, -7). We will do this using the Pythagorean theorem. #d=sqrt((4-(-3))^2+(-2+8)^2+(2-(-7))^2)# #d=sqrt(230)# #d=15.165 # (distance units?) #s=15.165/2 = 7.5825 ?/s # We’re not done, but we have gone as far as we can go with the information provided. We can only solve for the numerical part of the solution here because the asker neglected to provide the distance units. Our answer is practically meaningless, without our distance units. For example, #7.5825 (nm)/s #, #7.5825 m/s #, #7.5825 (km)/s # are very different speeds compared to each other. Units are VERY important to indicate. Think of it terms of disk space on your laptop, tablet or cell phone. A byte (indicated by B) is a unit of memory. A device with 30 GB of memory is much more valuable than a device with only 30 MB of memory. A megabyte, MB, is only 1 million bytes (think a 1-minute long video in mpeg format) compared to a GB, which is 1 billion--- that’s a 1000 times more space for music, videos, etc.! Units can be just as important as the numerical answer, or maybe even more- something to keep in mind.

Carson Alexander · Answer

undefined To find the speed of the object, calculate the distance traveled between the two points using the distance formula in three-dimensional space. Then divide the distance by the time taken to travel.