Solving Calc-Based Physics Problems: Object Position and Velocity at t=2s

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The discussion revolves around solving a physics problem involving an object's position as a function of time, given by the equation r=12ti+(15t-5.0t^2)jm. For part A, the position at t=2 seconds is found by substituting t into the equation. Part B requires calculating the average velocity over the interval from t=0 to t=2 seconds using the change in position over time, while part C necessitates finding the instantaneous velocity at t=2 seconds through differentiation. There is some confusion regarding the need for derivatives, particularly for calculating average velocity. The conversation emphasizes the importance of correctly applying the relevant equations for each part of the problem.
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Homework Statement



An objects position as a function of time is given by r=12ti+(15t-5.0t^2)jm, where t is time in seconds. A: what is the onject's position at t=2 s. B what is its average velocity in the interval from t=o to t=2.0s.C: what is its instantaneous velocity at t=2?

Homework Equations



Derivative:12i+(15-10t)

V=change in r/change t

The Attempt at a Solution


A: simply plug 2 in for t in the original equation
B:take the derivative of the problem and plug in 2 for t
C: Dont really know . . .
 
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possum30540 said:
A: simply plug 2 in for t in the original equation
OK.
B:take the derivative of the problem and plug in 2 for t
No derivatives needed, since you want the average velocity. (Use the formula you quoted.)
C: Dont really know . . .
Here's where you need a derivative.
 
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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