An object travels North at #6 m/s# for #9 s# and then travels South at #6 m/s# for #7 s#. What are the object's average speed and velocity?
The average speed is 6m/s; the average velocity is 0.75 m/s North.
First, we must determine the displacement of the object during each time interval.
During the first 9s
During the next 7s
For the average speed , we consider only the total distance travelled and the total time taken
For the average velocity , we consider the net displacement and the time taken. The net displacement has been only 12 m North.
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Average Speed: ( \frac{{\text{{Total Distance}}}}{{\text{{Total Time}}}} )
Average Velocity: ( \frac{{\text{{Displacement}}}}{{\text{{Total Time}}}} )

Calculate total distance traveled: [ \text{{Total Distance}} = (\text{{Distance North}}) + (\text{{Distance South}}) ]

Calculate displacement: [ \text{{Displacement}} = (\text{{Distance North}})  (\text{{Distance South}}) ]

Calculate average speed: [ \text{{Average Speed}} = \frac{{\text{{Total Distance}}}}{{\text{{Total Time}}}} ]

Calculate average velocity: [ \text{{Average Velocity}} = \frac{{\text{{Displacement}}}}{{\text{{Total Time}}}} ]
Given the values for time, velocity, and direction, substitute into the formulas to find the average speed and velocity.
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When evaluating a onesided 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 onesided 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 onesided 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 onesided 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.
 What is #(60. ms^2)/(0.060s) #?
 An object has a mass of #4 kg#. The object's kinetic energy uniformly changes from #12 KJ# to # 72KJ# over #t in [0,5s]#. What is the average speed of the object?
 An object travels North at # 3 m/s# for #7 s# and then travels South at # 4 m/s# for # 4 s#. What are the object's average speed and velocity?
 An object has a mass of #5 kg#. The object's kinetic energy uniformly changes from #150 KJ# to # 16KJ# over #t in [0,8s]#. What is the average speed of the object?
 What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = 6t# from #t in [0, 2]#?
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