# What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = t/4+2# from #t in [0, 6]#?

Delta x is equal to int_0^6(1/8t^2+2t)d t.

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The average speed is 9 units per time interval.

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- An object is at rest at #(2 ,1 ,6 )# and constantly accelerates at a rate of #1/4 m/s^2# as it moves to point B. If point B is at #(3 ,2 ,7 )#, how long will it take for the object to reach point B? Assume that all coordinates are in meters.
- An object's two dimensional velocity is given by #v(t) = ( e^t-2t , 2t-4e^2 )#. What is the object's rate and direction of acceleration at #t=a #?
- A car with an initial speed of #6.5# #m##/##s# accelerates at a uniform rate of #0.92# #m##/##s^2# for #3.6# #s#. What is the final speed and the displacement of the car during this time?
- If an object with uniform acceleration (or deceleration) has a speed of #4 m/s# at #t=2# and moves a total of 25 m by #t=6#, what was the object's rate of acceleration?
- An object has a mass of #1 kg#. The object's kinetic energy uniformly changes from #48 KJ# to #36 KJ# over #t in [0, 3 s]#. What is the average speed of the object?

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