Forces- Centripetal acceleration

AI Thread Summary
The shape of the graph representing centripetal acceleration as a function of time varies based on the object's motion. For uniform circular motion, the graph is a straight line indicating constant centripetal acceleration. In contrast, for accelerated circular motion, the graph takes the form of an upward-opening parabola. The specific shape ultimately depends on the nature of the motion being analyzed. Understanding these relationships is crucial for accurately depicting centripetal acceleration in different scenarios.
majormuss
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Homework Statement


What is the Shape of graph that represents Centripetal acceleration as a function of time?


Homework Equations





The Attempt at a Solution


I know its a parabola, but am not sure how the curve is going to look.
 
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A graph of centripetal acceleration vs. time could look like anything you want, depending on how the object moves. If it's moving in a straight line, for example, the graph would be a horizontal line at a=0
 
majormuss said:
What is the Shape of graph that represents Centripetal acceleration as a function of time?

Centripetal acceleration of what? :confused:
 
if the body is undergoing uniform circular motion, then the graph should be a straight line.
if the body is undergoing accelerated circular motion, then the graph should be a parabola- open upwards and vice-versa
 
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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