An object is at rest at #(4 ,5 ,8 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(7 ,9 ,2 )#, 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 · 2016-05-09T13:04:45

Find the distance, define the motion and from the equation of motion you can find the time. Answer is:

#t=3.423# #s#

Firstly, you have to find the distance. The Cartesian distance in 3D environments is:

#Δs=sqrt(Δx^2+Δy^2+Δz^2)#

Assuming the coordinates are in form of #(x,y,z)#

#Δs=sqrt((4-7)^2+(5-9)^2+(8-2)^2)#

#Δs=7.81# #m#

The motion is acceleration. Therefore:

#s=s_0+u_0*t+1/2*a*t^2#

The object starts still #(u_0=0)# and the distance is #Δs=s-s_0#

#s-s_0=u_0*t+1/2*a*t^2#

#Δs=u_0*t+1/2*a*t^2#

#7.81=0*t+1/2*4/3*t^2#

#t=sqrt((3*7.81)/2)#

#t=3.423# #s#