An object is at rest at $(2 ,9 ,5 )$ and constantly accelerates at a rate of $7/6 m/s$ as it moves to point B. If point B is at $(6 ,3 ,7 )$ , how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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Answer 1 · 2018-05-30T08:13:33

The time is $=3.58s$

The distance $AB$ is

$AB=sqrt((6-2)^2+(3-9)^2+(7-5)^2)=sqrt(16+36+4)=sqrt(56)m$

Apply the equation of motion

$s=ut+1/2at^2$

The initial velocity is $u=0ms^-1$

The acceleration is $a=7/6ms^-2$

Therefore,

$sqrt56=0+1/2*7/6*t^2$

$t^2=12/7sqrt56$

$t=sqrt(12/7sqrt56)=3.58s$

An object is at rest at (2 ,9 ,5 )(2 ,9 ,5 ) and constantly accelerates at a rate of 7/6 m/s7/6 m/s as it moves to point B. If point B is at (6 ,3 ,7 )(6 ,3 ,7 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.