An object is at rest at $(4 ,1 ,8 )$ and constantly accelerates at a rate of $7/5 m/s^2$ as it moves to point B. If point B is at $(2 ,9 ,1 )$ , 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 · 2017-11-29T19:13:22

The time is $=3.93s$

The distance $AB$ is

$AB=sqrt((2-4)^2+(9-1)^2+(1-8)^2)=sqrt(4+64+49)=(sqrt117)m$

Apply the equation of motion

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

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

The acceleration is $a=7/5ms^-2$

Therefore,

$sqrt117=0*1/2*7/5*t^2$

$t^2=10/7sqrt117$

$t=sqrt(10/7sqrt117)=3.93s$

An object is at rest at (4 ,1 ,8 )(4 ,1 ,8 ) and constantly accelerates at a rate of 7/5 m/s^27/5 m/s^2 as it moves to point B. If point B is at (2 ,9 ,1 )(2 ,9 ,1 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.