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sry i need help again ,but if possible with full steps this time cuz exam is tomorrow and i got 2 sleep now ,so i check the answer just b4 i leave
i attached the problem in the topic

Um... the velocity function reaches zero when time approaches infinity, so the ball never stops...

And in response to your other question in the other thread, if you're not allowed to use a calculator, then you have to first find the zeros of the equation (which I don't know how they expect you to know how to do that) and then integrate the positive parts then add that to the absolute value of the integral of the negative parts.

what about distance in first 10 secs ? and how to integrate it in first place

Well you know that the function of acceleration is the second derivative of the position function, thus it's the first derivative of the velocity function. Derive the acceleration function to get v(t)=(10/cuberoot{7.5x+1))+C and you know that C=10 m/s so you have v(t)=(10/cuberoot{7.5x+1))+10. So take the integral of (10/cuberoot{7.5x+1))+10 from 0 to 10 seconds.

Edit: Since you derived acceleration to get velocity, you know that the first half of your integral integrates back into the velocity function and that the +10 at the end integrates into 10x, then just plug in numbers. (I don't think the function ever goes to negative, at least it doesn't look like it. If it does, integrate the absolute value of the function with a calculator or find the zeros and add the absolute value of the negative integral to the positive one)

Lets see how it goes.

What you need to solve this:
You have to know how to integrate, derivate, etc.

Im too lazy, so i WONT DO THIS for you fully, just some hints.

Gl:)

*maniac laughter*

http://kepfeltoltes.hu/view/090311/3091 ... es.hu_.jpg

Edit:
If you dont succed, just ask me nicely and i do this for you, also i give you some free lessons how to integrate, derivate, and thus, how to set up differential equations and how to solve them. But with this stuff you just need some practice, not a serius business.

Edit2: Sm is right about this particle.It wont stop ever(more coming, checking the funtcions again)
Edit3: Actualy im solving this right now couldnt resist it...
Sry dude, have to close this netcafee... next time then... and gl doing the exam.