Hello, I have found the questions below in a textbook and would really appreciate some help in solving them. I have attempted to answer both parts but do not really understand how to comprehensively answer the questions, so I believe that my answers must be wrong. if anyone could be of help i would enormously appreciate it 👍😊
A particle of mass 200g moves with a velocity of 2t-t^2ms^-1, at t seconds from when it is at rest at the origin.
I do understand that if you know s as a function of time, one can find the velocity by differentiation i.e. v=ds/dt
And that you can obtain the acceleration by differentiating velocity with respect of time ie. a=dv/dt=d^2s/dt^2
1.Find an expression in terms of t for the force acting on the particle.
I really do not know where to start, would I use Newton's second law
F=ma
and since it has been established that m=200 find a in terms of;
a=dv/dt
a=2-t
F=200*(2-t)
F=400-200t
Or a=v-u/t
a= 2t-t^2/t
a=2-t
F=200*(2-t)=400-200t
2. Find the time when the particle next passes through the origin
I honestly do not know where to begin, would this be where t=d^2s/dt^2 is of use?
Or since the particle is at rest at the origin does this mean;
v(t)=2t-t^2=0
Solving the quadratic 2t+t^2+0=0
t=2 and t=0
So the particle would pass through the origin again at t=2s, or is this calculating when the particle comes to rest? Sorry I am really confused