- #1
ztalira
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Homework Statement
A point mass,m, is constrained to move in one-dimension and is acted on buy a force that depends on time in the following way:
F[x](t)=ƒ[o]+αt+βt^2
where ƒo,α, and β are constants . In terms of the quantities given, answer the following:
If the object starts off at rest at t=0, find its velocity at a later time, t[f]
Find the distance the mass has traveled from t=0 to t=t[f]
Homework Equations
v=at
F=ma
The Attempt at a Solution
I believe I found the velocity at t[f] by, having
a=F/m then
v=(F/m)t
and for t[f]
v[f]=((ƒ[o]+αt[f]+βt[f]^2)/(m))*t[f]but from there, I'm kinda stuck.
I know that the distance must be the integral of the velocity, but, with velocity changing, how can I find the integral?
Or is there perhaps another way?