What equation could I use for this?

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AI Thread Summary
To determine when Particle B passes Particle A, the relevant equation is Δx = vit + 1/2at², which calculates displacement based on initial velocity and acceleration. Both particles start at the same point and move in the same direction, with Particle A having an initial velocity of 6.9 m/s and an acceleration of 1.8 m/s², while Particle B has an initial velocity of 2.4 m/s and an acceleration of 5.7 m/s². Setting the displacement equations for both particles equal to each other allows for solving the time at which they meet. The user initially struggled with the calculations but later found the correct answer. Understanding the need for displacement in this context is crucial for solving the problem effectively.
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Homework Statement



Two particles are at the same point at the same time, moving in the same direction. Particle A has an initial velocity of 6.9 m/s and an acceleration of 1.8 m/s2. Particle B has an
initial velocity of 2.4 m/s and an acceleration of 5.7 m/s2.

At what time will B pass A?

Homework Equations



\Deltax = vit + 1/2at2

The Attempt at a Solution



I'm just wondering what equation I should use for this. I think I need to set up a system, but I don't see why I would need displacement for this. The only information the question gives us is vi for both, the acceleration for both, and the fact that they're going the same direction.

I really don't understand how I would go about solving it. Knowing the equation(s) to use would be a great start!

I'm really discouraged. I just tried setting two equations equal and I got the wrong answer... I don't know what to do.

Thank you so much!

EDIT: I calculated with the quadratic equation wrong somehow, but found the answer.
 
Last edited:
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AVReidy said:
...

I'm just wondering what equation I should use for this. I think I need to set up a system, but I don't see why I would need displacement for this. The only information the question gives us is vi for both, the acceleration for both, and the fact that they're going the same direction.
...
One more piece of information.

When B passes A, they're at the same location.
 
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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