An object is at rest at #(4 ,5 ,1 )# 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.

1 Answer
May 10, 2016

Answer:

2.77s

Explanation:

The coordinate of initial position of the object is#(x_1=4,y_1=5,z_1=1)#

The coordinate of final position of the object is#(x_2=7,y_2=9,z_2=2)#

Initial velocity of the object#u=0#
Acceleration #a=4/3m/s^2#

Distance traversed #s= sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)#
#=sqrt((7-4)^2+(9-5)^2+(2-1)^2))#
#=sqrt(9+16+1)=sqrt26=5.1m#
If the time required be t sec then
#s=ut+1/2*a*t^2=0*t+1/2*4/3*t^2##=>5.1=2/3*t^2#
#t=sqrt(15.3/2)=2.77s#