# What is the average speed of an object that is moving at #30 m/s# at #t=0# and accelerates at a rate of #a(t) =5-2t^2# on #t in [0,5]#?

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To find the average speed, you need to calculate the total distance traveled and divide it by the total time taken. To find the total distance, integrate the velocity function over the given time interval. Then divide this total distance by the total time taken.

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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.

- A projectile is shot from the ground at a velocity of #6 m/s# and at an angle of #(7pi)/12#. How long will it take for the projectile to land?
- An object has a mass of #5 kg#. The object's kinetic energy uniformly changes from #15 KJ# to # 64KJ# over #t in [0,12s]#. What is the average speed of the object?
- An object is at rest at #(1 ,2 ,9 )# and constantly accelerates at a rate of #1 m/s^2# as it moves to point B. If point B is at #(6 ,1 ,3 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- The position of an object moving along a line is given by #p(t) = t - 3sin(( pi )/3t) #. What is the speed of the object at #t = 4 #?
- An object's two dimensional velocity is given by #v(t) = ( 5t-t^3 , 3t^2-2t)#. What is the object's rate and direction of acceleration at #t=4 #?

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