# Math Help - Velocity and position

1. ## Velocity and position

If s(t) = (1/3)(t^3) - (3/2)(t^2) - 18t
During what time is the object moving towards the origin?
I know I set s(t)v(t) < 0, but from there on I’m a little stuck.

When the velocity is 10m/s, find its displacement.
My answers to this were : -511/6, and 208/3
Is this correct?

How many times does the object cross a marker on the line located at s = 20?
I’m not sure how to do this one.

Any help is appreciated.

2. Originally Posted by Shapeshift
If s(t) = (1/3)(t^3) - (3/2)(t^2) - 18t
During what time is the object moving towards the origin?
I know I set s(t)v(t) < 0, but from there on I’m a little stuck.

When the velocity is 10m/s, find its displacement.
My answers to this were : -511/6, and 208/3
Is this correct?

How many times does the object cross a marker on the line located at s = 20?
I’m not sure how to do this one.

Any help is appreciated.
$\frac{ds}{dt} = v < 0 \Rightarrow t^2 - 3t - 18 < 0 \Rightarrow (t - 6)(t + 3) < 0$.

A graph of $v = (t - 6)(t + 3)$ makes it clear that the object is moving to the left for $0 < t < 6$ and moving to the right for $t > 6$.

Now note that at t = 0 the object is at s = 0.

3. so for the last question where i have to find how many times the object crosses s=20

i set s(t) = 20, giving me 20 = (1/3)(t^3) - (3/2)(t^2) - 18t

after bringing the 20 over and finding the lowest common denominator, i get

2t^3 - 9t^2 -108t -120 = 0

i tried using the factor theorem, but nothing seems to work out.

4. Originally Posted by Shapeshift
so for the last question where i have to find how many times the object crosses s=20

i set s(t) = 20, giving me 20 = (1/3)(t^3) - (3/2)(t^2) - 18t

after bringing the 20 over and finding the lowest common denominator, i get

2t^3 - 9t^2 -108t -120 = 0

i tried using the factor theorem, but nothing seems to work out.
Are you allowed to draw a graph to answer the question ....? If so, it's clear that there's only one value of t greater than zero.