An object is at rest at #(7 ,8 ,4 )# and constantly accelerates at a rate of #5/4 m/s^2# as it moves to point B. If point B is at #(1 ,5 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
May 28, 2016

Answer:

It takes 3.29 seconds.

Explanation:

First of all we need to know how much distance the objects has to travel. The distance between two points is given by the Pitagora's theorem in 3 dimensions

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

in our case

#d=sqrt((7-1)^2+(8-5)^2+(4-3)^2)=sqrt(36+9+1)=sqrt(46)\approx6.78m#

Now that we know that our body will travel for 6.78 m we can use the equation of motion for an accelerating body that is

#x=1/2at^2#

where #x# is the traveled distance, for us 6.78, #a# is the acceleration, for us #5/4m/s^2# and #t# is the time that we want to find. I plug the values in the equation

#6.78=1/2*5/4*t^2#
#6.78=5/8t^2#

I am interested in #t# so I multiply both sides for #8/5# and do the square root

#sqrt(6.78*8/5)=t#
#t=sqrt(10.848)\approx 3.29# s.