Relationship between velocity and stopping distance

AI Thread Summary
The discussion focuses on the relationship between velocity and stopping distance, emphasizing the need to understand the forces involved in stopping a moving object. It highlights that a force must be applied opposite to the direction of motion, resulting in deceleration as described by Newton's second law. Key variables include initial velocity, negative acceleration, and final velocity at rest. The conversation suggests using dynamics equations to quantify this relationship. Understanding these principles is essential for calculating stopping distances effectively.
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Homework Statement



Determines the relationship between velocity and stopping distance linking this to the force applied on the passenger or pedestrian, quantitatively.

Homework Equations





The Attempt at a Solution



I have not found any so please provide relevant equations and examples so I can understand.
 
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In order to stop a moving object a force has to be applied against the direction of motion. That force, when applied to the object would cause an acceleration in the direction opposite to the direction of motion of the moving object by Newton's second law. That would mean the object in effect decelerates. You have the initial velocity, the negative acceleration and the final velocity (at rest). From here you should be able to see how to write a few equations using some formulae from dynamics and Newton's laws.
 
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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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