At time t=0, two cars are next to one another on a long straight road. The functions that give their distance traveled (in feet) after t minutes are called A(t) and B(t). We are not given these formulas, however. We are given the formulas and graphs for their instantaneous speeds: AYt)-32-16t+23 and B'(t)=2t+8. B'(0 A'(1) time (minutes) (a) Find the times at which the two cars have the same instantaneous speed. earlier time: t= minutes later time: tw minutes (b) Which of the following are true? (HINT: Remember that the cars are in the same place at t=0 and the graphs above are of the cars' instantaneous speeds.) Select all that apply. At t-0, the A-car is traveling 23 feet per minute. The cars are getting closer together during the first minute of travel (from t=0 to t=1). The cars are getting farther apart during the first minute of travel (from t-0 to t-1). The A-car is getting faster during the first minute of travel (from t-0 to te1). The B-car is getting faster during the first minute of travel (from t=0 to t=1). Since the distance graphs are not given, we can't determine whether the cars are getting farther apart or closer together during the first minute of travel. (c) Which of the following is true? (Select only one.) The A-car is ahead of the B-car at t=1 minute. Since we don't have the graphs of distance traveled, we can't determine which car is ahead at t=1 minute. The B-car is ahead of the A-car at t-1 minute. The cars are next to each other at t=1 minute. (d) At what time is the speed of the A-car lowest? t= minutes (e) What is the speed of the B-car the second time the two cars have the same speed? feet per minute speed (fUmin)
At time t=0, two cars are next to one another on a long straight road. The functions that give their distance traveled (in feet) after t minutes are called A(t) and B(t). We are not given these formulas, however. We are given the formulas and graphs for their instantaneous speeds: AYt)-32-16t+23 and B'(t)=2t+8. B'(0 A'(1) time (minutes) (a) Find the times at which the two cars have the same instantaneous speed. earlier time: t= minutes later time: tw minutes (b) Which of the following are true? (HINT: Remember that the cars are in the same place at t=0 and the graphs above are of the cars' instantaneous speeds.) Select all that apply. At t-0, the A-car is traveling 23 feet per minute. The cars are getting closer together during the first minute of travel (from t=0 to t=1). The cars are getting farther apart during the first minute of travel (from t-0 to t-1). The A-car is getting faster during the first minute of travel (from t-0 to te1). The B-car is getting faster during the first minute of travel (from t=0 to t=1). Since the distance graphs are not given, we can't determine whether the cars are getting farther apart or closer together during the first minute of travel. (c) Which of the following is true? (Select only one.) The A-car is ahead of the B-car at t=1 minute. Since we don't have the graphs of distance traveled, we can't determine which car is ahead at t=1 minute. The B-car is ahead of the A-car at t-1 minute. The cars are next to each other at t=1 minute. (d) At what time is the speed of the A-car lowest? t= minutes (e) What is the speed of the B-car the second time the two cars have the same speed? feet per minute speed (fUmin)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Transcribed Image Text:At time t=0, two cars are next to one another on a long straight road. The functions that give their distance traveled (in feet) after t minutes are called A(t) and B(t). We are not given these formulas, however. We are given the formulas and graphs for their instantaneous speeds:
A'(t)=3t2-16t+23 and B'(t)=2t+8.
B'(t)
(A'(t)
time (minutes)
(a) Find the times at which the two cars have the same instantaneous speed.
earlier time: t=
minutes
later time: t=
minutes
(b) Which of the following are true? (HINT: Remember that the cars are in the same place at t=0 and the graphs above are of the cars' instantaneous speeds.)
Select all that apply.
O At t=0, the A-car is traveling 23 feet per minute.
O The cars are getting closer together during the first minute of travel (from t=0 to t=1).
O The cars are getting farther apart during the first minute of travel (from t=0 to t=1).
O The A-car is getting faster during the first minute of travel (from t=0 to t=1).
O The B-car is getting faster during the first minute of travel (from t=0 to t=1).
O Since the distance graphs are not given, we can't determine whether the cars are getting farther apart or closer together during the first minute of travel.
(c) Which of the following is true? (Select only one.)
O The A-car is ahead of the B-car at t=1 minute.
o Since we don't have the graphs of distance traveled, we can't determine which car is ahead at t=1 minute.
O The B-car is ahead of the A-car at t=1 minute.
O The cars are next to each other at t=1 minute.
(d) At what time is the speed of the A-car lowest?
t=
minutes
(e) What is the speed of the B-car the second time the two cars have the same speed?
feet per minute
speed (ft/min)
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