Solve for Position: Physics Question with Initial Position and Velocity

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To solve for the position of a particle with an initial position of X=0m and an initial velocity of v=-6.0m/s, given its acceleration function of [1.0 m/s^2 + (0.25 m/s^3)t], calculus is necessary to determine when the velocity reaches zero. The process involves integrating the acceleration function to find the velocity function and then setting it to zero to solve for time. Once the time is found, integrating the velocity function will yield the position at that instant. Without a grasp of calculus, alternative graphical methods may provide insights, but they won't yield precise answers. Understanding the geometric concepts behind integration can aid in approaching the problem even without formal calculus knowledge.
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A particle has an initial position X=0m and an initial velocity v=-6.0m/s. Its acceleration is given by the function [1.0 m/s^2 + (0.25 m/s^3)t] where t is in seconds.

Use calculus to find the position of the particle at the instant when its velocity is zero.


-this is a bonus question on an assignment..its a bonus because we haven't started calculus yet, therefore I have no idea how to do it.

Thanks
 
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If you don't know any calculus, you can't really do it... unless you do it graphically and knew what the geometric idea behind integration is without really having to know what integration is.
 
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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