An object is at rest at #(1 ,6 ,9 )# and constantly accelerates at a rate of #1# # ms^-2# as it moves to point B. If point B is at #(6 ,4 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

Question

1231 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-06-07T12:33:57

The distance is #8.06# #m#, and the object will take #4.01# #s# to travel this distance.

First we need to find the distance between the two points:

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

#s=sqrt((6-1)^2+(4-6)^2+(3-9)^2)#

#s=sqrt((5)^2+(-2)^2+(-6)^2)#

#s=sqrt(25+4+36) = sqrt(65) = 8.06# #m# (assuming the units are in metres)

Then we can use #s = ut + 1/2 at^2#

The initial velocity, #u#, is equal to #0#, so the first term disappears.

#s = 1/2 at^2#

Rearranging:

#t=sqrt((2s)/a)=sqrt((2(8.06))/1)=4.01# #s#