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Substituting the known quantities, we have that 15 minutes is 15/60, or 1/4, or 0.25 of an hour. We will now
make a new list of the quantities with the appropriate units:
− _
d
v =

t d = 22 km
_ t = 0.25 h
50.0 km
=
0.667 h −
v = ?
_
km

= 75.0

h These quantities are related in the average speed equation,
which is already solved for the unknown average velocity:
2.3 Weight is the gravitational force on an object. Newton’s second
d
law of motion is F = ma, and since weight (w) is a force (F), − _
v =

then F = w and the second law can be written as w = ma. Th e t
acceleration (a) is the acceleration due to gravity (g), so the Substituting the known quantities, we have
equation for weight is w = mg. A kilogram is a unit of mass and
2
22 km
g is known to be 9.8 m/s , so − _
v =

0.25 h
w = mg _
km

m _
(
2)
h
= (5.2 kg) 9.8 = 88
s
2.7. List the quantities with their symbols.
kg·m
_
= (5.2)(9.8) − v = 3.0 × 10 m/s
8
s 2
t = 20.0 min
= 50.96 N
d = ?
= 51 N
We see that the velocity units are meters per second, but the
2.4 List the known and unknown quantities.
time units are minutes. We need to convert minutes to seconds,
m = 40.0 kg and
m _
8

a = 2.4 − v = 3.0 × 10 m/s
s 2
3
t = 1.20 × 10 s
F = ?
d = ?

These are the quantities found in Newton’s second law of
motion, F = ma, which is already solved for force (F). Th us, These relationships can be found in the average speed equation,

which can be solved for the unknown:
F = ma
d
m _
v = ∴ d =
(

2)
= (40.0 kg) 2.4 − _ t v − t
s
8 m _ 3

kg·m
_ d = ( 3.0 × 10 ) (1.20 × 10 s)
s

= (40.0)(2.4)
s 2 8+3 m _

= (3.0)(1.20) × 10 × s

s
= 96 N
11
= 3.6 × 10 m
2.5 List the known and unknown quantities. 8
= 3.6 × 10 km
F = 100.0 N F _
F = ma ∴ a = 2.8. Listing the quantities with their symbols, we can see the
m
m = 5.00 kg problem involves the quantities found in the defi nition of
kg·m
_
a = ? 100.0 average speed:
2
_
s

= − v = 350.0 m/s
5.00 kg
_ kg·m 1 t = 5.00 s
100.0 _ _

= ×
5.00 s 2 kg d = ?
d
m _ − _ v −
v = ∴ d = t

= 20.0 t
s 2
m _

2.6. Listing these quantities given in this problem, with their d = ( 350.0 ) (5.00 s)
s
symbols, we have m _

= (350.0)(5.00) × s
s
d = 22 km
= 1,750 m
t = 15 min
− v = ?

The usual units for a speed problem are km/h or m/s, and the

problem specifies that the answer should be in km/h. We see
E-3 APPENDIX E Solutions for Group A Parallel Exercises 645