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

Rate of accelaration is

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The object's acceleration at ( t = 1 ) is ( (2, -\sin(\pi) - 3) ), or simply ( (2, -3) ). The rate of acceleration is 2 units per second squared in the horizontal direction, and 3 units per second squared in the vertical direction, downward.

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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 #6 kg#. The object's kinetic energy uniformly changes from #54 KJ# to #150 KJ# over #t in [0, 8 s]#. What is the average speed of the object?
- An object travels North at # 8 m/s# for #3 s# and then travels South at # 7 m/s# for # 8 s#. What are the object's average speed and velocity?
- If an object with uniform acceleration (or deceleration) has a speed of #6 m/s# at #t=0# and moves a total of 15 m by #t=2#, what was the object's rate of acceleration?
- If an object with uniform acceleration (or deceleration) has a speed of #4 m/s# at #t=0# and moves a total of 26 m by #t=9#, what was the object's rate of acceleration?
- Why is speed classiﬁed as a scalar quantity and velocity classiﬁed as a vector quantity?

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