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 ,5 ,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 · 2016-08-01T21:10:12

The distance to be covered is #sqrt2# #m#, and this takes #0.96# #s#.

First find the distance to be covered:

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

#d=sqrt((2-1)^2+(5-5)^2+(6-5)^2)=sqrt(1^2+0^2+1^2)=sqrt2# #m#

Now we can use the equation:

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

But the initial velocity #u=0#, so #s = 1/2 at^2#

Rearranging to make #t# the subject:

#t=sqrt((2s)/a) = sqrt(2xxsqrt2)/(7/4) = 0.96# #s#.