# An object's two dimensional velocity is given by #v(t) = ( 3t^2 - 5t , -t^3 +4t )#. What is the object's rate and direction of acceleration at #t=1 #?

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The object's acceleration at ( t = 1 ) is ( (6, -2) ) and its rate of acceleration is ( \sqrt{40} ) units per second squared.

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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.

- An object has a mass of #12 kg#. The object's kinetic energy uniformly changes from #96 KJ# to # 160 KJ# over #t in [0, 4 s]#. What is the average speed of the object?
- An object is at rest at #(2 ,8 ,6 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,5 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- A train is moving at a constant velocity of #"5 m/s"#. After it exists a tunnel, it starts to accelerate with an acceleration of #"9 m/s"^2# for #"5 s"#. What is the velocity of the train after #"5 s"# ?
- An object is at rest at #(2 ,8 ,6 )# and constantly accelerates at a rate of #5/3 m/s^2# as it moves to point B. If point B is at #(7 ,5 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- An object is at rest at #(3 ,5 ,1 )# and constantly accelerates at a rate of #4/3 m/s^2# as it moves to point B. If point B is at #(7 ,9 ,2 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.

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