# Thread: Calculus Applications help

1. ## Calculus Applications help

The function of a moving object is s(t) = t^5/2(7-t) t >= 0 in metres and at time t in seconds

After how many seconds of the motion of the object change?

when does the direction of motion of the object change?

When is its acceleration positive?

I got the velocity and the acceleration of the object, but I do not know how to get what these questions are asking me.

2. Think about what changing vel and acc mean. If the vel is positive, what direction is the object moving? If it goes from positive to negative, what does that mean about direction of motion? s'' = acc so solve it that way

3. Motion changes when S changes its sign.
so use S< 0 and solve for t.

For acceleration positive use $d^2 S/dt >0$ ( to be precise solve $d^2 S/dt = 0$)

4. Originally Posted by arpitagarwal82
Motion changes when S changes its sign.
so use S< 0 and solve for t.
Yes but the question said the direction of motion, which could be it is still moving forward but acceleration the opposite direction.

5. Originally Posted by Jameson
Yes but the question said the direction of motion, which could be it is still moving forward but acceleration the opposite direction.
Thanks for reminding.

Motions changes when v changes its direction.
Direction changes when S changes its sign.

IS that ok now?

6. Originally Posted by arpitagarwal82
Thanks for reminding.

Motions changes when v changes its direction.
Direction changes when S changes its sign.

IS that ok now?
That was my point exactly.

7. direction of motion is determined by the sign of velocity ... period.

### the position of a function of a moving object is s(t)=t^5/2(7-t), t>0, in metres, at time t, in seconds. when is its acceleration positive

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