3. Suppose you are traveling at 50mph. (a) How far do you travel in 1/2 hour? (b) If v(t) represents your velocity at time t, then v(t) = 50 (the function is constant). Sketch v(t) on the interval [0, 1]. (c) What is the area under the curve of v(t) on the interval [0,]?
3. Suppose you are traveling at 50mph. (a) How far do you travel in 1/2 hour? (b) If v(t) represents your velocity at time t, then v(t) = 50 (the function is constant). Sketch v(t) on the interval [0, 1]. (c) What is the area under the curve of v(t) on the interval [0,]?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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![3. Suppose you are traveling at 50 mph.
(a) How far do you travel in 1/2 hour?
(b) If \( v(t) \) represents your velocity at time \( t \), then \( v(t) = 50 \) (the function is constant). Sketch \( v(t) \) on the interval \([0, 1]\).
(c) What is the area under the curve of \( v(t) \) on the interval \([0, \frac{1}{2}]\)?
(d) How far do you travel after \( t \) hours? Write down a function \( d(t) \) which represents the distance traveled after \( t \) hours. Sketch \( d(t) \) on the interval \([0, 1]\). What is \( d(\frac{1}{2}) - d(0) \)?
(e) How do the functions \( v(t) \) and \( d(t) \) relate? (Hint: derivatives)
(f) In your sketch of \( d(t) \), what is the slope of the tangent line at \( t = \frac{1}{2} \)? Does it equal \( d'(\frac{1}{2}) \)? Does it equal \( v(\frac{1}{2}) \)?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F2a874603-d28a-4420-b369-9729c939fed8%2F3bad8cec-8c35-47e4-b4e4-285bb7a7cfcd%2F4d1grft_processed.jpeg&w=3840&q=75)
Transcribed Image Text:3. Suppose you are traveling at 50 mph.
(a) How far do you travel in 1/2 hour?
(b) If \( v(t) \) represents your velocity at time \( t \), then \( v(t) = 50 \) (the function is constant). Sketch \( v(t) \) on the interval \([0, 1]\).
(c) What is the area under the curve of \( v(t) \) on the interval \([0, \frac{1}{2}]\)?
(d) How far do you travel after \( t \) hours? Write down a function \( d(t) \) which represents the distance traveled after \( t \) hours. Sketch \( d(t) \) on the interval \([0, 1]\). What is \( d(\frac{1}{2}) - d(0) \)?
(e) How do the functions \( v(t) \) and \( d(t) \) relate? (Hint: derivatives)
(f) In your sketch of \( d(t) \), what is the slope of the tangent line at \( t = \frac{1}{2} \)? Does it equal \( d'(\frac{1}{2}) \)? Does it equal \( v(\frac{1}{2}) \)?
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