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