1. Dimensional Analysis Contents:
Handy things to know
Ways to convert
Whiteboard practice

3. Hand out Formula sheet

4. Ways to convert units: Unit cancellation: 30. mph to ft/s:
Calculator’s built in (TI 85/86)
Conversion factors
Google
Ways to convert units:
Unit cancellation:
30. mph to ft/s:
30. mi(5280 ft)( 1 hr )
hr ( 1 mi )(3600 s)
= 44 f/s (note the units canceling)
Calculator (TI 85/86)
2nd CONV, MORE, MORE, SPEED, 30 mi/hr > ft/s
Conversion factor:
30. mph to ft/s: (1 mph = 1.47 f/s)
30. mph x (1.47) = 44.1 = 44 ft/s
(slightly off - what’s the “real” conversion factor?)
Google:
Type 30. mph in ft/s into Google

5. Whiteboards:
Conversions
1 | 2 | 3 | 4 | 5

6. Convert 32 mile/hour to feet/second
5280 ft = 1 mi
3600 s = 1 hr
32 mi(5280 ft)( 1 hr ) =
hr ( 1 mi )(3600 s)
47 f/s (2 sig figs)
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
47 f/s

7. Convert 88.0 feet/second to mph
5280 ft = 1 mi
3600 s = 1 hr
88 ft( 1 mi )(3600 s) = 60 mph
s (5280 ft)( 1 hr )
60.0 mph
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
60.0 mph

8. Convert 27.2 m/s to km/hr 1000 m = 1 km 3600 s = 1 hr
27.2 m ( 1 km )(3600 s) = km/hr
s (1000 m)( 1 hr )
97.9 km/hr
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
97.9 km/hr

9. Convert 110. km/hr to m/s 1000 m = 1 km 3600 s = 1 hr
110 km (1000 m)( 1 hr ) = m/s
hr ( 1 km )(3600 s)
30.6 m/s
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
30.6 m/s

10. A car traveling 80. km/hr will go how far (in meters) in 2.7 seconds?
1000 m = 1 km
3600 s = 1 hour (60x60)
(km/hr)/(3.6) = m/s
80. km/hr(1000m/km)(3600s/h) = m/s
v = s/t
22.22 m/s = x/(2.7 s)
s = (22.22 m/s)(2.7 s) = 60 m= 60. m
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
60. m

11. A car goes 132 feet in 3. 1 seconds
A car goes 132 feet in 3.1 seconds. What is its speed in miles per hour?
v = s/t
v = (132 f)/(3.1 s) = f/s
f/s(3600 s/h)/(5280 f/mi) = 29 mph
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
170 f

12. A Baseball going 75 mph takes how much time to go 90. feet?
75 mi/hr(5280 ft/1 mi)(1 hr/3600 s) =
110 f/s
v = s/t
110 f/s = (90. f)/t
t = (90. f)/(110 f/s) = s = .82 s
Shortcuts: (mph = miles/hour)
1 m/s = 3.6 km/hr  mph  ft/s
1 mph  f/s ( …)  km/hr  m/s
1 f/s = m/s  mph ( …)  km/hr
1 km/hr  m/s  mph  ft/s
.82 s

14. Write these down while you wait:
1 hr = 60 min = 3600 sec
1 km = 1000 m  mile
1 mile = 5280 ft = 1760 yards  1609 m
1 m  ft
1 yard = 3 feet
Shortcuts:
1 m/s = 3.6 km/hr  mph, (mph = miles/hour)
1 mph  1.47 f/s ( …)
1 f/s  .682 mph ( …)
Answer This Question:
How many feet per second is 30 mph? (use any method you want – including help from others – but have an answer)

15. Write these down while you wait:
1 hr = 60 min = 3600 sec
1 km = 1000 m  mile
1 mile = 5280 ft = 1760 yards  1609 m
1 m  ft
1 yard = 3 feet
Shortcuts:
1 m/s = 3.6 km/hr  mph, (mph = miles/hour)
1 mph  1.47 f/s ( …)
1 f/s  .682 mph ( …)
Answer This Question:
How many feet per second is 30 mph? (use any method you want – including help from others – but have an answer)
(30 mph)( ) = 44 ft/s
(30 mi)(5280 ft)(1 hr) = 44 ft/s
( hr )( 1 mi )(3600 s)