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The position of an object moving along a line is given by #p(t) = 3t - tcos(( pi )/3t) #. What is the speed of the object at #t = 5 #?

Answer 1

Julia Aguilar

#s(5) ~~ -2.0 #

Given: #p(t) = 3t - tcos(pi/3t)#

The speed is the first derivative:

#s(t) = 3 - cos(pi/3t) + pi/3tsin(pi/3t) #

#s(5) ~~ -2.0 #

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Answer 2

Isabella Alvarez

To find the speed, calculate the absolute value of the derivative of the position function and then substitute t = 5.

[ |p'(t)| = |3 + \frac{\pi}{3} \sin\left(\frac{\pi}{3t}\right)| ]

[ \text{Speed at } t = 5: |p'(5)| ]

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Answer from HIX Tutor

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.