Particle Position @t=0 to t=8 sec: I'm Wrong?

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The discussion centers on calculating the displacement of a particle from its initial position at t=0 to t=8 seconds. The original poster mistakenly considers velocity instead of displacement, leading to confusion. Participants clarify that the correct approach involves analyzing the area under the velocity vs. time graph to determine displacement. The relationship between an object's position change and the geometry of the graph is emphasized as crucial for accurate calculations. Understanding these concepts is essential for solving the problem correctly.
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You are looking for a displacement, not a velocity, which is what you answer is.

You have a velocity graph and have to find a displacement from it?

What is the relationship between the change in an objects position, and the geometry of a velocity vs. time graph?
 
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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