When throwing an object into the air, is acceleration equal to -9.81 throughout the entire process?

In short, no. This is because to get the object to go upwards, you have to create an upwards acceleration with your hand as you throw it up into the air. If you didn't create this acceleration, the object would just immediately drop the second you let go of it, entering free fall at -9.81 m/s^2.

However, unlike the short acceleration the object has because of your hand, the gravitational pull on the object is pretty much a constant acceleration of -9.81 m/s^2 (I say almost because if you go high enough into the atmosphere, the force of gravity will lessen, but that's not the point here). 

The second the ball leaves your hand, it no longer has the acceleration that your hand has provided, meaning the only acceleration it's getting is from gravity. This is why when you throw a ball into the air, it eventually slows down, reaching a velocity of 0 m/s at a special point called the apex before it comes plummeting back down towards Earth.

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