Does anybody know the answer to this physics problem?

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The physics problem involves calculating the speed and acceleration of a pebble on a bicycle wheel with a diameter of 54.0 cm, which spins three times per second. To find the speed, the distance covered by the pebble in one second must be determined, considering the wheel's circumference. The original poster struggled with rounding errors in their calculations but eventually arrived at the correct answer. The discussion highlights the importance of precision in mathematical problem-solving. Ultimately, the poster resolved the issue after multiple attempts and appreciated the input from others.
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Homework Statement



Ive have tried it so many times but can't get the right answer but the problem is: Your roommate is working on his bicycle and has the bike upside down. He spins the 54.0 cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What is the particles speed? and then what is the particles acceleration?

Homework Equations





The Attempt at a Solution

 
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How have you attempted this problem? If it goes by 3 times every second, how much distance is it covering in 1 second?
 
Yes, but after a couple of different attempts, i finally got the answer, it turns out my rounding was off by a couple of digits. But thanks anyways
 
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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