A particle of mass M , initially at rest at x=0, is accelerated by a force that increases in time as F=CT^2.

Determine its velocity v as a function of time.

Question

A particle of mass M , initially at rest at x=0, is accelerated by a force that increases in time as F=CT^2.

Determine its velocity v as a function of time.

anonymous · Answer

F(x)=V

irishboy123 · Answer

start with Newton: F = ma.
got that?

that leaves a = F/m or,.....
a(t) = F(t)/m, as you gave a force that varies with time as opposed to the usual Newtonian constant force (and constant acceleration).  the same formula holds true BTW, if the Force at time t is F(t), then the acceleration will be F(t)/m.

in your case we know that F(t) = ct^2

therefore we know something about the acceleration, don't we?  a(t) = ?!?!

now, you will need to integrate to switch from acceleration to velocity because d(velocity)dt = acceleration: or S (acceleration) dt = velocity.  

feel free to let me know how you get on.