# An object is thrown vertically from a height of #12 m# at # 19 ms^-1#. How long will it take for the object to hit the ground?

Assuming the object was thrown downward, the time taken will be

We are aware of:

Given that both the initial velocity and the acceleration are pointing downward, we are selecting that direction as the positive direction.

Put the quadratic back in standard form:

Using the quadratic formula or any other method of your choice, solve the quadratic equation; this will yield two roots, but only one of them makes sense:

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The time it takes for the object to hit the ground is approximately 2.19 seconds.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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- An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #128 KJ# to # 48 KJ# over #t in [0, 12 s]#. What is the average speed of the object?
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- An object has a mass of #8 kg#. The object's kinetic energy uniformly changes from #24 KJ# to # 64KJ# over #t in [0, 3 s]#. What is the average speed of the object?
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