A particle of mass 40

Question

40kg moves in a straight line such that the force (in newtons) acting on it at time,t (in seconds) is given by, 160t^4-320t^2-360

at time t=0, v is given by v(0)=10, and its position x is given by x(0)=14. What is the position of the particle at time t?

I have that v(t) will be ((4t^5/5)-(8t^3/3)-9t+v0)

Bit stick where to go from here?

Answer 1

Now, use the fact that v(0) = 10
(4t^5/5)-(8t^3/3)-9t+v0 = 10 at t=0
So, v0 = 10, and thus

v(t) = (4t^5/5)-(8t^3/3)-9t+10

Now go on to x(t), using x(0) to find the constant of integration.