How Does Displacement Affect Final Velocity in Constant Acceleration?

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The discussion focuses on calculating the final velocity of a car that starts from rest and accelerates at a constant rate, with an initial displacement of x and a final velocity of v. To find the final velocity when the displacement is increased to 9x, participants suggest using the kinematic equation v^2 = vo^2 + 2a(x - xo). The problem is approached in two parts, first determining v for the initial displacement and then adjusting for the increased displacement. The conversation emphasizes understanding the relationship between displacement and final velocity in constant acceleration scenarios. Overall, the exchange highlights the importance of breaking down the problem into manageable steps for clarity.
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Homework Statement



A car starts from rest, accelerates at a constant rate, has a displacement of x and a final velocity of v. What is the final velocity (in terms of v) if the displacement was 9x?

Homework Equations


v^2=vo^2 + 2a(x-xo)


The Attempt at a Solution


I have no idea. :(
 
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Hello KJD, welcome to PF! You must have some idea! :smile:.
Seems like a 2-part problem. First find v, given:
A car starts from rest, accelerates at a constant rate, has a displacement of x and a final velocity of v.

What would v be in this case, using the equation you provided?

What is the final velocity in terms of v if the displacement was 9x?

Now, jack up x by 9, using your result from the first part. Does this help?
 
Thank you so much! I think I understand now! I just didn't know where to start. Thanks again :smile:
 
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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