An object is at rest at $(5 ,2 ,1 )$ and constantly accelerates at a rate of $2/5 m/s$ as it moves to point B. If point B is at $(6 ,9 ,2 )$ , 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 · 2018-07-03T06:22:13

The time is $=5.98s$

The distance $AB$ is

$d_(AB)=sqrt((6-5)^2+(9-2)^2+(2-1)^2)$

$=sqrt(1^2+7^2+1^2)$

$=sqrt(1+49+1)$

$=sqrt(51)m$

The acceleration is $a=2/5ms^-2$

The initial velocity $u=0$

Apply the equation of motion

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

$sqrt(51)=0+1/2*2/5*t^2$

$t^2=5sqrt(51)$

$t=sqrt(5sqrt(51))=5.98s$

The time is $=5.98s$

An object is at rest at (5 ,2 ,1 )(5 ,2 ,1 ) and constantly accelerates at a rate of 2/5 m/s2/5 m/s as it moves to point B. If point B is at (6 ,9 ,2 )(6 ,9 ,2 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.