What is the average speed, on #t in [0,5]#, of an object that is moving at #7 m/s# at #t=0# and accelerates at a rate of #a(t) =t^2-2t# on #t in [0,4]#?
The average speed is
The speed is the integral of the acceleration
Then,
Therefore,
The average speed is
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The average speed of the object on the interval [0,5] is 8.5 m/s.
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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.
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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- A projectile is shot from the ground at a velocity of #3 m/s# at an angle of #pi/4#. How long will it take for the projectile to land?
- An automobile rolls down an incline, traveling #s(t) = 6t^2 + 3# feet in #t# seconds. What is the velocity at #t = 2#, and after how many seconds will the velocity be #30# #f##/##sec#?
- A driver is driving around a circular track at a speed of 45 m/h. How is the driver's velocity compared to his acceleration?

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