Initial Velocity and Acceleration: A Curious Conundrum

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Initial velocity can be zero even when acceleration is present, as demonstrated by the example of a ball held in hand before being dropped. While the ball experiences a downward acceleration of 9.8 m/s² due to gravity, it remains stationary until released. Acceleration is defined as the change in velocity over time, meaning that an object can start from rest and still have a non-zero acceleration. The discussion clarifies that initial acceleration does not imply initial velocity; rather, acceleration is necessary to initiate movement from a state of rest. Understanding this concept is crucial for grasping the relationship between velocity and acceleration in physics.
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How is V(initial) = 0 when Acc at start is equal to 4m/s^2

shouldnt there be some type of Velocity?
 

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Nope.

Lets say you drop a ball from your hand. The acceleration is 9.8m/s^s downward, but when the ball is in your hand it is not moving. (unless of course you are swinging your arm).

So at initial, the very beginning, there is no velocity. Velocity changes due to acceleration.
 
I thought this was only true for "free falling" objects...

For example... I posted some graphs...
graph 1 is velocity increasing... then graph 2 is acceleration based off graph 1...


However if velocity had a constant slope say y = 3.. then acc would be zero...
My thoughts where... if initial acceleration is not zero in word problem then initial velocity must not be zero... which i showed in my two graphs...
Obviously I am wrong.. I just need to wrap my mind around it ..
 

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Acceleration is a change in velocity during some time interval. In order for any object to begin moving from rest, whatever the direction of travel, the object must undergo acceleration.

When you are in a car stopped at a traffic light, and the car takes off after the light changes, the force you feel pushing you into the seat back is due to the car accelerating away from the traffic light.
 
Thank you..
 
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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