An object is at rest at #(7 ,3 ,9 )# and constantly accelerates at a rate of #7/4 ms^-2# as it moves to point B. If point B is at #(2 ,5 ,8 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Answer 1 · 2018-01-23T22:05:21

First we find the distance between the points, which is #5.5# m, then calculate the time taken, which is #2.5# s.

Find the distance between the points:

#s=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#

#s=sqrt((7-2)^2+(5-3)^2+(9-8)^2)#

#s=sqrt(5^2+2^2+1^2)=sqrt(30)=5.5# m

Now to find the time taken:

#s=ut+1/2at^2#

The initial velocity, #u#, is just equal to #0# because the object is initially at rest, so this reduces to:

#s=1/2at^2#

#t=sqrt((2s)/a)=sqrt((2xx5.5)/(7/4))=2.5# s