# Calculus Applications help

• Feb 26th 2009, 03:49 PM
mathamatics112
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.
• Feb 26th 2009, 04:24 PM
Jameson
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
• Feb 26th 2009, 04:34 PM
arpitagarwal82
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 $d^2 S/dt = 0$)
• Feb 26th 2009, 04:36 PM
Jameson
Quote:

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.
• Feb 26th 2009, 04:45 PM
arpitagarwal82
Quote:

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?
• Feb 26th 2009, 04:47 PM
Jameson
Quote:

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. (Clapping)
• Feb 26th 2009, 05:45 PM
skeeter
direction of motion is determined by the sign of velocity ... period.