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 #?
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To find the speed of the object at ( t = 4 ), you need to calculate the absolute value of the derivative of the position function ( p(t) ) with respect to time ( t ) at ( t = 4 ). So, compute ( |p'(4)| ), where ( p'(t) ) is the derivative of ( p(t) ) with respect to ( t ).
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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.
- If an object with uniform acceleration (or deceleration) has a speed of #12 m/s# at #t=0# and moves a total of 145 m by #t=15#, what was the object's rate of acceleration?
- An object's two dimensional velocity is given by #v(t) = ( t^2, t-t^2sin(pi/3)t)#. What is the object's rate and direction of acceleration at #t=4 #?
- An object is thrown vertically from a height of #12 m# at # 19 ms^-1#. How long will it take for the object to hit the ground?
- What is the average speed of an object that is still at #t=0# and accelerates at a rate of #a(t) = t^3-2t+2# from #t in [2, 3]#?
- Lauren's SUV was detected exceeding the posted speed limit of 60 kilometers per hour, how many kilometers per hour would she have been traveling over the limit if she had covered a distance of 10 kilometers in 5 minutes?

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