68. For each rate, we use distance d = vt and convert to SI using 0.0254 cm = 1 inch (from which we derive

the factors appearing in the computations below).

(a) The total distance d comes from summing

d

1

=

120

steps

min



0.762 m/step

60 s/min



(5 s) = 7.62 m

d

2

=

120

steps

min



0.381 m/step

60 s/min



(5 s) = 3.81 m

d

3

=

180

steps

min



0.914 m/step

60 s/min



(5 s) = 13.72 m

d

4

=

180

steps

min



0.457 m/step

60 s/min



(5 s) = 6.86 m

so that d = d

1

+ d

2

+ d

3

+ d

4

= 32 m.

(b) Average velocity is computed using Eq. 2-2: v

avg

= 32/20 = 1.6 m/s, where we have used the fact

that the total time is 20 s.

(c) The total time t comes from summing

t

1

=

8 m



120

steps

min

 

0.762 m/step

60 s/min

 = 5.25 s

t

2

=

8 m



120

steps

min

 

0.381 m/step

60 s/min

 = 10.5 s

t

3

=

8 m



180

steps

min

 

0.914 m/step

60 s/min

 = 2.92 s

t

4

=

8 m



180

steps

min

 

0.457 m/step

60 s/min

 = 5.83 s

so that t = t

1

+ t

2

+ t

3

+ t

4

= 24.5 s.

(d) Average velocity is computed using Eq. 2-2: v

avg

= 32/24.5 = 1.3 m/s, where we have used the

fact that the total distance is 4(8) = 32 m.