# Integral problem question (energy and momentum)

#### Yura

i got a sheet full of alot of questions on integrations and differentiations and got them all except for two of them. in both the questions i run into the same type of problem so if i get one then i can probably work out the other using the same method.
here's the question that's troubling me:

(i've worked out part a) but i cant seem to get out part b). )

a particle with mass 80g is acted on by a force which decreases uniformly with respect to displacement from 10N to zero over 2 metres.

a) calculate the maximum velocity of the particle, given v(0) = 0.

b) find the time for which the force becomes zero.

the part a) answer that i got was 9m/s.
for the part b) its like im missing some information but seeing as there's two questions like that on the sheet im guessing theres a method to do this. what i think i need is a function of the Force to x so that i can use
dx/dt = dx/dF * dF/dt.
but unless i have that infomation, right now im clueless on how to continue.

EDIT: i've done a little more on it but i ended up with the integral of
(-62.5x^2 + 250x)^(-1-2) dx ... but i dont know how to do this integration.

much appreciated if someone can show me how this is done.
thanks.

Last edited:

#### HallsofIvy

Homework Helper
" what i think i need is a function of the Force to x so that i can use
dx/dt = dx/dF * dF/dt."

But you are given that! F(x) is linear because "F decreases uniformly from 2 N to 0 over 2 meters".
Like any linear function, F can be written as F(x)= ax+ b and you know that
F(0)= 10, F(2)= 0.

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