Determining the Force acting on a Particle

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To determine the force acting on a particle moving in the XOY plane, the derivative of the movement equation must be calculated to find velocity, followed by another derivative for acceleration, which is then applied to Newton's Second Law. The individual is struggling with the problem and has attempted to evaluate it at t=0 and t=1 to derive vectors for velocity. There is a clear need for assistance in understanding the correct approach to solving the problem. The discussion highlights the challenge of reversing the process from force to position. Overall, the focus is on applying calculus and Newton's laws to solve for the force on the particle.
kacete
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Homework Statement


A particle of mass
kg.jpg
moves across the XOY plane following the equation:


Homework Equations


eq.jpg



The Attempt at a Solution


I'm totally clueless about this one.
I know I have to find the derivative of the movement equation to find the velocity and then again to find the acceleration and use it on Newton's Second Law of motion.
(The previous exercise was the reverse problem, given the F(t) eq, find the x(t) eq.)
I tried t=0 and t=1, and given the resulting vectors the velocity could be found? :frown:
 
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Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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