An object is at rest at #(8 ,2 ,9 )# and constantly accelerates at a rate of #3 m/s# as it moves to point B. If point B is at #(6 ,7 ,3 )#, 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 · 2017-03-19T13:28:20

The time is #=2.32s#

We are going to apply the following equation of motion :

#s=u_0t+1/2at^2#

#u_0=0#

So,

#s=1/2at^2#

#a=3ms^-2#

The distance between 2 points #A=(x_1,y_1,z_1)# and #B=(x_2.y_2.z_2)# is

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

Here,

#A=(8,2,9)# and #B=(6,7,3)#

So,

#s=sqrt((6-8)^2+(7-2)^2+(3-9)^2)#

#=sqrt(4+25+36)#

#=sqrt65#

From the equation of motion,

#t^2=(2s)/a#

#t^2=(2*sqrt65)/(3)=5.37#

#t=sqrt5.37=2.32s#