CK-12-Physics - Intermediate

2.3. Average Speed, Velocity, and Instantaneous Velocity http://www.ck12.org

Check Your Understanding

FIGURE 2.10

The car speeds up along its trip.

1. The first part of a trip is traveled at a speed of 40 mph for 1.5 hours and the second part of the trip is traveled at a
   speed of 60 mph for three hours. What is the average speed for the trip?

Answer:

v=

total distance

time

=

( 40 × 1. 5 + 60 × 3 )

( 1. 5 + 3 )

= 53

1

3

mph

FIGURE 2.11

The George Washington Bridge connecting New York and New Jersey.

2. A person travels across the George Washington Bridge (GWB) across the Hudson River between New Jersey and
   New York at 25 mph and returns at 40 mph. What is the average speed for the round trip?

Answer:There is no mention of the length of the bridge. The information is probably unnecessary. What is known?
The length of the bridge is the same regardless of which way it is traversed. Call the length of the bridgeL. Since
we don’t know the time that it takes for each trip over the bridge, let’s call the time going:t 1 and the time returning
t 2. We use the definition for average speed:v=total distancetotal time

The distance going can be expressed as:L= 25 t 1 , and the distance returning can be expressed as

L= 40 t 2. Solving each of these equations for time, permits the time of each trip to be expressed as:

t 1 = 25 L andt 2 = 40 L. The total distance for the trip isL+L= 2 L. Therefore:

Total distance

total time =

( 2 L)

( 25 L+ 40 L).

NoticeLLcan be factored out of the equation, which means the length is irrelevant to the problem’s solution as we
had surmised. A bit of algebraic rearranging gives us:

2

251 + 401 =

2

( 2540 )( 40 )+( 2525 )( 4 )=^2

[( 25 )( 40 )

( 25 + 40 )

]

= 30. 769 = 30 .8 mph