1. ## particle moving

A particle of mass 6 kg starts from rest and is subject to a force which increases uniformly from 0N to 12N in a time of 20s. prove the acceleration of the particle is t/10 m/s^2 seconds after it begins to move. prove that after the particle has moved a distance s meters when its speed is v m/s then
9s^2 =20v^3

I am not sure how to set this up. I can not use f=ma or P=FV

2. ## Re: particle moving

There are very few problems in physics where you can't use $F=m a$

This is not one of them.

You're given mass. You're given force as a function of time. Therefore you are given acceleration as a function of time.

The rest is a bit of straightforward calculus.

3. ## Re: particle moving

So this is what I did

so the force varies over time and we not one of the conditions. so I said F=Kt where k is a constant which we do not know and t is time. so the question says the force is 12N when t is20

so 12=20k 3/5 =k so then using F=ma 3/5 *t =6a a=t/10

I then let dv/dt and I let the upper limits be t and v and I rearranged to get t=√(20v)

so i then let t/10 = v dv/ds and I subbed in t=√(20v) and I integrated this and I got a useless expression. I thought I did every thing right and I can not see where I went wrong

4. ## Re: particle moving

Originally Posted by edwardkiely
So this is what I did

so the force varies over time and we not one of the conditions. so I said F=Kt where k is a constant which we do not know and t is time. so the question says the force is 12N when t is20

so 12=20k 3/5 =k so then using F=ma 3/5 *t =6a a=t/10

I then let dv/dt and I let the upper limits be t and v and I rearranged to get t=√(20v)

so i then let t/10 = v dv/ds and I subbed in t=√(20v) and I integrated this and I got a useless expression. I thought I did every thing right and I can not see where I went wrong
ok so you got $a(t) = \dfrac {t}{10}$

simple calculus gets you

$v(t) = \dfrac{t^2}{20}$

$s(t) = \dfrac{t^3}{60}$

$v(T) = V$

$T^2 = 20V$

$T = \sqrt{20V}$

$s(T) = S$

$T^3 = 60S$

$T = (60S)^{1/3}$

$(20V)^{1/2} = (60S)^{1/3}$

$8000V^3 = 3600S^2$

$20V^3 = 9S^2$

thank you