An object is at rest at $(1 ,5 ,5 )$ and constantly accelerates at a rate of $7/4$ $ms^-2$ as it moves to point B. If point B is at $(2 ,5 ,6 )$ , 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 · 2016-08-01T21:10:12

The distance to be covered is $sqrt2$ $m$ , and this takes $0.96$ $s$ .

First find the distance to be covered:

$d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)$

$d=sqrt((2-1)^2+(5-5)^2+(6-5)^2)=sqrt(1^2+0^2+1^2)=sqrt2$ $m$

Now we can use the equation:

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

But the initial velocity $u=0$ , so $s = 1/2 at^2$

Rearranging to make $t$ the subject:

$t=sqrt((2s)/a) = sqrt(2xxsqrt2)/(7/4) = 0.96$ $s$ .

An object is at rest at (1 ,5 ,5 )(1 ,5 ,5 ) and constantly accelerates at a rate of 7/47/4 ms^-2ms^-2 as it moves to point B. If point B is at (2 ,5 ,6 )(2 ,5 ,6 ), how long will it take for the object to reach point B? Assume that all coordinates are in meters.