Constant Motion Vs. Acceleration

AI Thread Summary
The discussion revolves around a scenario where a motorcyclist travels at a constant speed of 15 m/s while a police officer accelerates from rest at 3 m/s² to catch him. Participants suggest using equations of motion to equate the displacements of both the motorcyclist and the police officer to determine the time and distance involved in the chase. One participant calculates the time to be 18.75 seconds and the displacement to be 140.625 meters, although they express confusion about the results. The conversation emphasizes the importance of correctly applying kinematic equations to solve for the variables in question.
jessicayin22
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Homework Statement


A reckless motorcyclist drives past a school zone at a constant speed of 15 m/s , where the speed limit is only 10 m/s. at the same moment a police officer chases the motorcyclist from rest and accelerating at the rate of 3 m/s?
a. how fardoes the police travel before catching up to the motorcyclist?
b. how much time does it take the police car to catch up to the motorcyclist?
c. how fast is the police car traveling when it catches the motorcyclist?

Homework Equations


V(bar)=d/t, a= deltaV/t,

The Attempt at a Solution


okay, so i know that displacement is equal to each other, I've set the equations equal to each other and then solved for t...??
 
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jessicayin22 said:

Homework Statement


A reckless motorcyclist drives past a school zone at a constant speed of 15 m/s , where the speed limit is only 10 m/s. at the same moment a police officer chases the motorcyclist from rest and accelerating at the rate of 3 m/s?

Homework Equations


V(bar)=d/t, a= deltaV/t,


The Attempt at a Solution


do not know how to start...

You have a question mark, but have not actually asked a question.

I assume you want to know when the policeman catches the motorcyclist.

You could draw/sketch velocity time graphs of the situation and instantly see the answer.

Displacement of the reckless one is 15t

Displacement of the policeman follows "the equations of motion with constant acceleration" and one of them is really appropriate.

The displacements will of course be equal.
 
i set the equation and found out T= 18.75? ... but it doesn't make sense since the displacement eauals 140.625m
 
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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