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PHYS 2211 Solution Recitation 01 Week of January 14
Example
You have a 400 km trip back to Tech after break. You are able to drive at 100 km/hr for the first half of the time. Traffic gets worse as you approach Atlanta, so you are only able to drive at 60 km/hr for the second half of the time.
How much time did your trip take?
Let the first half of your trip, at speed v 1 , cover a distance d 1 and require time t 1. Similarly, let the second half of your trip, at speed v 2 , cover a distance d 2 and require time t 2. Let the total distance be D and the total time be T.
D = d 1 + d 2 = v 1 t 1 + v 2 t 2
Since t 1 and t 2 are each half the time, t 1 = t 2.
D = v 1 t 2 + v 2 t 2 = (v 1 + v 2 ) t 2 ⇒ t 2 =
D
v 1 + v 2
400 km 100 km/hr + 60 km/hr
= 2.5 hr
But t 2 is half the time, so the total time is 5 hr.
PHYS 2211 Solution Recitation 01 Week of January 14
Problem
You have a 4 hr trip back to Tech after break. You are able to drive at 100 km/hr for the first half of the distance. Traffic gets worse as you approach Atlanta, so you are only able to drive at 60 km/hr for the second half of the distance.
How much distance did your trip cover?
Let the first half of your trip, at speed v 1 , cover a distance d 1 and require time t 1. Similarly, let the second half of your trip, at speed v 2 , cover a distance d 2 and require time t 2. Let the total distance be D and the total time be T.
T = t 1 + t 2 =
d 1 v 1
d 2 v 2
Since d 1 and d 2 are each half the distance, d 1 = d 2.
T =
d 2 v 1
d 2 v 2
v 1
v 2
d 2 ⇒ d 2 =
T
1 v 1 +^
1 v 2
4 hr 1 100 km/hr +^
1 60 km/hr
= 150 km
But d 2 is half the distance, so the total distance is 300 km.
