Simple Acceleration and Velocity Problem

AI Thread Summary
The discussion revolves around a physics problem involving a train's position described by the equation x(t) = At^3 + Bt. Participants calculate the expressions for velocity and acceleration, determining that velocity is given by v = 3At^2 + B and acceleration by a = 6At. The values for constants 'A' and 'B' are found to be 1/15 and 5, respectively, based on the conditions of acceleration and velocity at t=5 seconds. The accuracy of the calculations is confirmed by other participants, who acknowledge a previous math error. Overall, the problem-solving process emphasizes understanding the relationships between position, velocity, and acceleration in kinematics.
veronicak5678
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Homework Statement


A train travels along a straight track. Its position is given by x(t) = At^3 + Bt from t = 0 to t=5.0 s.
a- find an expression for the velocity.
b- find an expression for the acceleration.
c- if the train has an acceleration of 2.00 m/s^2 and a velocity of 10.0 m/s at t=5, find 'A' and 'B'.


Homework Equations



v= dx/dt

a = dv/dt

The Attempt at a Solution



I got 3At^2 + B for velocity and 6At for acceleration. I got (1/15) for 'A' and 5 for 'B'. I don't have a book yet and just wanted to make sure i understand what I'm doing. Any help would be appreciated!
 
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Looks good to me.
 
Sorry, I don't know what you mean...
 
veronicak5678 said:
Sorry, I don't know what you mean...

No you did it right. I made a hasty math mistake.
 
Great. Thanks for your help!
 
I'm saying your answers are correct. :smile:

EDIT: methinks I missed something here :rolleyes:
 
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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