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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

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BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

Nick starts jogging and runs faster and faster for 3 mintues, then be walks for 5 minutes. He stops at tm intersection for 2 minutes, runs fairly quickly for 5 minutes, then walks for 4 minutes.

(a) Sketch a possible graph of the distances Nick has covered after t minutes.

(b) Sketch a graph of ds/dt.

(a)

To determine

To sketch: The possible graph of the distance s Nick has covered after t minutes.

Explanation

Given:

Nick starts jogging and for the first 3 minutes, runs faster and faster, then he walks for 5 minutes.

He stops for 2 minutes at a point and runs fairly quickly for 5 minutes, then walks for 4 minutes.

Calculation:

First step:

Nick starts jogging and runs faster and faster for 3 minutes.

When Nick is jogging the distance travelled is low but distance travelled

increases rapidly when Neck starts running faster and faster.

This implies that graph of distance versus time is not a linear.

It will be a bit quadratic in shape.

Second step:

Nick walks for 5 minutes.

So, the distance travelled increases linearly.

This implies that graph of distance versus time is linear.

Third step:

Nick stops an intersection for 2 minutes...

(b)

To determine

To sketch: The graph of dsdt

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