An object is at rest at #(1 ,5 ,5 )# and constantly accelerates at a rate of #7/4 # #ms^-2# as it moves to point B. If point B is at #(2 ,3 ,6 )#, 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 · 2016-08-06T08:51:52

First find the distance between the points, then use #s=ut+1/2at^2# to find the time taken.

First find the distance between the points:

#r=sqrt((2-1)^2+(3-5)^2+(6-1)^2)=sqrt6~~2.45# #m#

Now use the formula:

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

The initial velocity, #u=0# #ms^-1#, so #s=1/2at^2#. We can rearrange to make #t# the subject:

#t=sqrt((2s)/a)=sqrt((2xx2.45)/(7/4))=sqrt(2.8)~~1.67# #s#