An object is at rest at (1 ,2 ,1 ) and constantly accelerates at a rate of 2/3 m/s as it moves to point B. If point B is at (4 ,9 ,5 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.

1 Answer
Sep 29, 2017

5.08 seconds

Explanation:

A(1,2,1) and B(4,9,5)
Displacement AB=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)
AB=sqrt((4-1)^2+(9-2)^2+(5-1)^2)=sqrt(3^2+7^2+4^2)
AB=sqrt(9+49+16)=sqrt74 m

Acceleration a=2/3 m/s^2
Initial Velocity u=0

Using Newton's Second Equation
S=ut+1/2at^2
S is displacement
sqrt74=0+1/2(2/3)t^2
2/3t^2=2sqrt74
t^2=3sqrt74
t=sqrt(3sqrt74)
t=5.08 "seconds"