An object starts at rest and moves along a horizontal path. It’s position, s, in meters, is given by $s(t)=t^3-9t^2+24t+5$ . Is the object moving away or towards the origin when t=3s?

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Answer 1 · 2018-07-07T22:52:13

Moving away from the origin

Given the position $s$ of object is the function of time $t$ given as

$s(t)=t^3-9t^2+24t+5$

Now, position of object at $t=0$ ,

$s(0)=0^3-9\cdot 0^2+24(0)+5=5$

The position of object at $t=3\ sec$

$s(3)=3^3-9\cdot 3^2+24(3)+5=23$

Since, the distance of object at $t=3\ sec$ is greater than that at $t=0$ hence the object is moving away from the origin

An object starts at rest and moves along a horizontal path. It’s position, s, in meters, is given by s(t)=t^3-9t^2+24t+5s(t)=t^3-9t^2+24t+5. Is the object moving away or towards the origin when t=3s?