2. NO Calculator allowed: Train A runs back and forth on an east-west section of railroad track. Train A's velocity, measured in meters per minute, is given by a differentiable function vд(t), where time t is measured in minutes. Select values for vд(t) are given in the table below. t (minutes) 0 2 5 8 12 VA (t) (meters/minute) 0 100 40-120-150 a) Find the average acceleration of train A over the interval 2≤t≤8. b) Do the data in the table support the conclusion that train A's velocity is -100 meters per minute at some time t with 5 < t < 8? Give a reason for your answer. c) At time t = 2, train A's position is 300 meters east of the Origin Station, and the train is moving to the east. Write an expression involving an integral that gives the position of train A, in meters from the Origin Station, at time t = 12. Use a trapezoidal sum with 3 subintervals indicated by the table to approximate the position of the train at time t = 12. d) A second train, train B, travels north from the Origin Station. At time t the velocity of train B is given by vB (t) = −5t² + 60t + 25, and at time t = 2 the train is 400 meters north of the station. Find the rate, in meters per minute, at which the distance between train A and train B is changing at time t = 2.
2. NO Calculator allowed: Train A runs back and forth on an east-west section of railroad track. Train A's velocity, measured in meters per minute, is given by a differentiable function vд(t), where time t is measured in minutes. Select values for vд(t) are given in the table below. t (minutes) 0 2 5 8 12 VA (t) (meters/minute) 0 100 40-120-150 a) Find the average acceleration of train A over the interval 2≤t≤8. b) Do the data in the table support the conclusion that train A's velocity is -100 meters per minute at some time t with 5 < t < 8? Give a reason for your answer. c) At time t = 2, train A's position is 300 meters east of the Origin Station, and the train is moving to the east. Write an expression involving an integral that gives the position of train A, in meters from the Origin Station, at time t = 12. Use a trapezoidal sum with 3 subintervals indicated by the table to approximate the position of the train at time t = 12. d) A second train, train B, travels north from the Origin Station. At time t the velocity of train B is given by vB (t) = −5t² + 60t + 25, and at time t = 2 the train is 400 meters north of the station. Find the rate, in meters per minute, at which the distance between train A and train B is changing at time t = 2.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:2. NO Calculator allowed: Train A runs back and forth on an east-west section of
railroad track. Train A's velocity, measured in meters per minute, is given by a
differentiable function vд(t), where time t is measured in minutes. Select
values for vд(t) are given in the table below.
t (minutes)
0 2 5
8
12
VA (t) (meters/minute) 0 100
40-120-150
a) Find the average acceleration of train A over the interval 2≤t≤8.
b) Do the data in the table support the conclusion that train A's velocity is
-100 meters per minute at some time t with 5 < t < 8? Give a reason
for your answer.
c) At time t = 2, train A's position is 300 meters east of the Origin Station,
and the train is moving to the east. Write an expression involving an
integral that gives the position of train A, in meters from the Origin
Station, at time t = 12. Use a trapezoidal sum with 3 subintervals
indicated by the table to approximate the position of the train at time
t = 12.
d) A second train, train B, travels north from the Origin Station. At time t
the velocity of train B is given by vB (t) = −5t² + 60t + 25, and at time
t = 2 the train is 400 meters north of the station. Find the rate, in
meters per minute, at which the distance between train A and train B is
changing at time t = 2.
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