Problems - Conversion within and between Systems of Units

Question 1:
Perform the following conversions:
a. 1.5 min to seconds
b. 2 x 10^-2 h to seconds
c. 0.005 s to microseconds
d. 0.16 m to millimeters
e. 0.00000012 s to nanoseconds
f. 4 x 10^8 s to days


Solution 1:
a. 1.5 min x 60 s /1 min = 90 s


b. 2 x 10^-2 h x 3600 s / 1 h = 72 s
c. 0.05 s * 1 microsecond / 10^-6 s
      = 50 x 10^3 microseconds
d. 0.16 m * 1000 mm / 1 m = 160 mm
e. 0.00000012 s x 1 ns / 10^-9 s= 120 ns
f. 4 x 10^8 s * 1 day/24 h * 1 h /3600 s
    = 4,629.63 days


Question 2:
Perform the following conversions between systems:
a. 100 in. to meters
b. 4 ft to meters
c. 6 lb to newtons
d. 60,000 dyn to pounds
e. 150,000 cm to feet
f. 0.002 mi to meters (5280 ft = 1 mi)


Solution 2:
a. 100 in.
= 100 in. x (1 m / 39.37 in.)
= 2.54 m

b. 4 ft
= 4 ft x (0.3048 m /1 ft)
= 1.22 m
c. 6 lb
= 6 lb x (4.45 N /1 lb)
= 26.7 N
d. 60,000 dyn
= 60,000 dyn x (2.248 x 10^-6 lb/1 dyn)
= 0.13 lb
e. 150,000 cm
= 150,000 cm x (1 ft/ 30.48 cm)
= 4,924.26 ft
f. 0.002 mi
= 0.002 mi x (5280 ft/1 mi) x (0.3048 m/1 ft) = 3.22 m

Question 3:
Convert 60 mph to meters per second.

Solution 3:
60 mph
= 60 mi/h x (1.609344 km/h / 1 mi/h) x (1000 m / 1 km) x (1 h / 3600 s)
= 26.82 m/s

Question 4:
Quarters are about 1 in. in diameter.
How many would be required to stretch from one end of a football field to the other (100 yd)?

Solution 4:
100 yd
= 100 yd x ( 3 ft / 1 yd) x ( 12 in. / 1 ft)
= 3600 in.
= 3600 quarters

Question 5:
Find the distance in meters that a mass traveling at 600 cm/s will cover in 0.016 h.

Solution 5:
d = ? m ; v = 600 cm/s ; t = 0.016 h
d = v x t
= 600 cm/s x (1 m / 100 cm) x 0.016 h x (3600 s / 1 h)
= 345.6 m

Question 6:
The record for the race is 10.22 min. There is a race up 86 floors. Each floor is 14 ft high.
What was the racer's speed in min/mi for the race?

Solution 6:
t = 10.22 min ;
d = 86 floors x (14 ft / 1 floor)
=  1,204 ft x (1 mi / 5280 ft)
= 0.2280 mi
v = d / t
=  1,204 ft / 10.22 min
= 0.0223 mi/min
1/v = 1 / (0.0223 mi/min)
= 44.82 min/mi