An object is at rest at $(4 ,5 ,6 )$ and constantly accelerates at a rate of $5/3 m/s^2$ as it moves to point B. If point B is at $(7 ,5 ,3 )$ , 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 · 2017-10-25T09:26:10

$" Appro. "2.26 sec.$

Suppose that, the object is at rest the point (pt.) $A=A(4,5,6).$

Its final position is at the pt. $B=B(7,5,3).$

Hence, using the distance (dist.) formula, the dist. travelled by

the object, i.e.,

$"Dist. "AB=sqrt{(7-4)^2+(5-5)^2+(3-6)^2}, or,$

$AB=s==sqrt18.$

Recall that, $s=ut+1/2at^2........(star),$

where,

$s"=dist., "u"=initial velocity, "t"=time, and, "a"=accelaration."$

In our case, $s=sqrt18, u=0, a=5/3.$ Sub.ing in $(star),$ we get,

$sqrt18=0+1/2*5/3t^2 :. t^2=(6*3sqrt2)/5=(3.6)(1.414),$

$t^2~~5.0912,$

$rArr t~~sqrt5.0912~~2.26 sec.$

An object is at rest at (4 ,5 ,6 )(4 ,5 ,6 ) and constantly accelerates at a rate of 5/3 m/s^25/3 m/s^2 as it moves to point B. If point B is at (7 ,5 ,3 )(7 ,5 ,3 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.