Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Can someone please help with a-d? Thank you.
**Braking Distance and Speed Analysis** **1) Introduction** The braking distance of a vehicle is defined as the distance traveled from where the brakes are applied to when the vehicle comes to a complete stop. The speed, \( s \) ms\(^{-1}\), and braking distance, \( d \) m, of a truck were recorded. This information is summarized in the following table: | Speed, \( s \) ms\(^{-1}\) | 0 | 6 | 10 | |-------------------------|----|----|----| | Braking distance, \( d \) m | 0 | 12 | 60 | **Model Development** This information was used to create a Model A, where \( d \) is a function of \( s \), \( s \geq 0 \). **Model A:** \[ d(s) = ps^2 + qs \] where \( p, q \in \mathbb{Z} \). At a speed of 6 ms\(^{-1}\), Model A can be represented by the equation \( 6p + q = 2 \). Additional data was used to create Model B, a revised model for the braking distance of a truck. **Model B:** \[ d(s) = 0.95s^2 - 3.92s \] The actual braking distance at 20 ms\(^{-1}\) is 320 m. **Tasks:** a) i) Write down a second equation to represent Model A, when the speed is 10 ms\(^{-1}\). ii) Find the values of \( p \) and \( q \). b) Find the coordinates of the vertex of the graph of \( y = d(s) \). c) Using the values in the table and answer to part (b), sketch the graph of \( y = d(s) \) for \( 0 \leq s \leq 10 \) and \( -10 \leq d \leq 60 \), clearly showing the vertex. d) Hence, identify why Model A may not be appropriate at lower speeds.
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Transcribed Image Text:**Braking Distance and Speed Analysis** **1) Introduction** The braking distance of a vehicle is defined as the distance traveled from where the brakes are applied to when the vehicle comes to a complete stop. The speed, \( s \) ms\(^{-1}\), and braking distance, \( d \) m, of a truck were recorded. This information is summarized in the following table: | Speed, \( s \) ms\(^{-1}\) | 0 | 6 | 10 | |-------------------------|----|----|----| | Braking distance, \( d \) m | 0 | 12 | 60 | **Model Development** This information was used to create a Model A, where \( d \) is a function of \( s \), \( s \geq 0 \). **Model A:** \[ d(s) = ps^2 + qs \] where \( p, q \in \mathbb{Z} \). At a speed of 6 ms\(^{-1}\), Model A can be represented by the equation \( 6p + q = 2 \). Additional data was used to create Model B, a revised model for the braking distance of a truck. **Model B:** \[ d(s) = 0.95s^2 - 3.92s \] The actual braking distance at 20 ms\(^{-1}\) is 320 m. **Tasks:** a) i) Write down a second equation to represent Model A, when the speed is 10 ms\(^{-1}\). ii) Find the values of \( p \) and \( q \). b) Find the coordinates of the vertex of the graph of \( y = d(s) \). c) Using the values in the table and answer to part (b), sketch the graph of \( y = d(s) \) for \( 0 \leq s \leq 10 \) and \( -10 \leq d \leq 60 \), clearly showing the vertex. d) Hence, identify why Model A may not be appropriate at lower speeds.
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Step 1: Given information
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Step 2: Part a) : Value of p & q
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Cross-checking the value of d(20) from model A & model B
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part b): Vertex of y = d(s)
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Part c) : Sketch of the model A
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part d) : Why model A is not suitable for lower velocities
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