Question

please help me with this

The rectilinear motion of a particle if given by 〖s=v〗^2-9 where s is in feet and v in feet per second. When t=0, s=0 and v= 3 fps. Find the s-t, v-t and a-t relations.

Answer 1

the equation is s= v^2 - 9

Answer 2

Do you have to use differential equations? I don't know if this is relevant at all. I don't understand this, sorry. But maybe this will help if it's in the right direction.

\(s=v^2-9\\\implies
v^2=s+9\\\implies
v=\left( s+9\right)^\frac{1}{2}\\\implies
\dfrac{ds}{dt}=\left( s+9\right)^\frac{1}{2}\\\implies
\dfrac{ds/dt}{\left( s+9\right)^{1/2}}=1\\\implies
\int\dfrac{ds/dt}{\left( s+9\right)^{1/2}}dt=t+c\\\quad
=\int\left( s+9\right)^{-\frac{1}{2}}ds=t+c
\)
And I don't know about the rest... But you'll have \(s(t)\), I think. And then you can take derivatives to get \(v(t)\) and \(a(t)\) maybe?

Answer 3

tnx @theEric

Answer 4

I hope I helped, but I really don't know what to do with this one! Good luck!

Answer 5

tnx