An object is at rest at #(3 ,0 ,2 )# and constantly accelerates at a rate of #7/5 m/s^2# as it moves to point B. If point B is at #(5 ,7 ,7 )#, 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 · 2017-08-06T06:22:50

#t ~~ 3.55 s#

#vec s_i = 3hati + 2hatk#

#vec s_f = 5hati + 7hatj + 7hatk#

#vec s = vec s_f - vec s_i#

#vec s = 2hati + 7hatj+ 5hatk#

#|vec s| = sqrt(2^2+7^2+5^2)#

#|vec s| = sqrt(78)#

#|vec s| = 8.83 m#

#|vec a| = 7/5 m*s^2#

#|vec u| = 0#

#|vec s| = |vec u|t + 1/2(|vec a|t^2)#

#rArr 8.83 = 0*t + 1/2*7/5*t^2#

#rArr 8.83 = 7/10t^2#

#rArr 88.3/7 = t^2#

#rArr t~~3.55 s#