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
P dilip_k
May 10, 2016

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 objectu=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

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