Explanation Given: We have to find the acceleration of the helicopter at time t = 5 min, which is at height s ( t ) = 300 t − 4 t 3 . Formula used: The acceleration of a body is the derivative of its velocity, where velocity is the derivative of its position. Therefore, we can say that the acceleration is the second derivative of the position. Thus, we have to use the Power Rule here and find the second derivative of the given position, s ( t ) = 300 t − 4 t 3 The Power Rule states that ( x n ) ' = n x n − 1 Calculation: We can find the derivatives of the given function using the Power Rule. Therefore, we get the derivatives as s ( t ) = 300 t − 4 t 3 v ( t ) = s ' ( t ) = 300 − 3 × 4 t 3 − 1 = 300 − 12 t 2 a ( To determine (b) To plot the graph in the given interval and show that the helicopter is slowing down during this interval

3rd Edition

ISBN: 9781464125263

Author: Jon Rogawski, Colin Adams

Publisher: W.H. Freeman & Co

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Question

Chapter 3.5, Problem 37E

To determine

(a)

The acceleration of a helicopter at the given time and from the given height.

To determine

(b)

To plot the graph in the given interval and show that the helicopter is slowing down during this interval

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Chapter 3.5, Problem 36E

Chapter 3.5, Problem 38E

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(a) The acceleration of a helicopter at the given time and from the given height.

Solution Summary: The author explains that the acceleration of a body is the derivative of its velocity, and the power rule states that s(t)=300t-4t3.