Practice Problems Key

ACSM Practice Problems

Answer Key

1. VO₂ = 0.1 ml^. kg^-1. min^-1 (horizontal speed) +1.8 ml^. kg^-1. min^-1(vertical speed)(fractional grade) + 3.5ml^. kg^-1. min^-1

7 METs x 3.5 = 24.5 ml^. kg^-1. min^-1

24.5 ml^. kg^-1. min^-1 = 0.1 ml^. kg^-1. min^-1 (horizontal speed) +1.8 ml^. kg^-1. min^-1(vertical speed)(.10) + 3.5ml^. kg^-1. min^-1

24.5 ml^. kg^-1. min^-1 -3.5ml^. kg^-1. min^-1 = 0.1 ml^. kg^-1. min^-1 (horizontal speed) +

1.8 ml^. kg^-1. min^-1(vertical speed)(.10) + 3.5ml^. kg^-1. min^-1

21 ml^. kg^-1. min^-1 = 0.1 ml^. kg^-1. min^-1 (speed) +.18 ml^. kg^-1. min^-1

21 ml^. kg^-1. min^-1 = .28 ml^. kg^-1. min^-1 (speed)

21 ml^. kg^-1. min^-1 /.28 ml^. kg^-1. min^-1 (speed)

speed = 75 m^. min^-1

speed = 75 m^. min^-1 / 26.8 m^. min^-1

speed 2.8 mph

2. VO₂ = 0.2 ml^. kg^-1. min^-1 (horizontal speed) + 0.9 ml^. kg^-1. min^-1(vertical speed)(fractional grade) + 3.5ml^. kg^-1. min^-1 -3.5ml^. kg^-1. min^-1

7 mph x 26.8 m^. min^-1 = 187.6 m^.min^-1

58 ml^. kg^-1. min^-1 x .85=49.3 ml^. kg^-1. min^-1

49.3 ml^. kg^-1. min^-1 = 0.2 ml^. kg^-1. min^-1 (187.6 m^. min^-1 )+1.8 ml^. kg^-1. min^-1

(187.6 m^. min^-1 )(fractional grade) + 3.5ml^. kg^-1. min^-1

Horizontal VO₂= 0.2 ml^. kg^-1. min^-1 (187.6 m^. min^-1) VO₂= 37.52 ml^. kg^-1. min^-1

Net VO₂= 49.3 ml^. kg^-1. min^-1- 37.52 ml^. kg^-1. min^-1 - 3.5ml^. kg^-1. min^-1

Net VO₂= 8.28 ml^. kg^-1. min^-1

8.28 ml^. kg^-1. min^-1=1.8 ml^. kg^-1. min^-1(187.6 m^. min^-1)(fractional grade)

8.28 ml^. kg^-1. min^-1=337.68(fractional grade)

8.28 ml^. kg^-1. min^-1/337.68(fractional grade)

fractional grade =0.025 x 100 = 2.5%

3. VO₂ = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1(work rate)/body mass

10 METs x 3.5 = 35 ml^. kg^-1. min^-1

35 ml^. kg^-1. min^-1= 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1(work rate)/47 kg

35 ml^. kg^-1. min^-1-7 ml^. kg^-1. min^-1 = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (work

rate)/47 kg-7 ml^. kg^-1. min^-1

28 ml^. kg^-1. min^-1x 47 kg = 1.8 ml^. kg^-1. min^-1(work rate)/47 kg x 47 kg

1316 ml^. min^-1/1.8= (work rate)

work rate=731 kp^. m^-1. min^-1

work rate = (resistance setting)(flywheel distance)(kpm)

731 kp^. m^-1. min^-1 = (resistance setting)(3 m)(50 kpm)

731 kp^. m^-1. min^-1 = (resistance setting)(150)

731 kp^. m^-1. min^-1/150= (resistance setting)(150)/150

resistance setting = 4.87 kp

4. VO₂ = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (work rate)/body mass

4.5 L^. min^-1x.60= 2.7 L^. min^-1x 1000=2700 ml^.. min^-1 /100 kg = 27 ml^. kg^-1. min^-1

27 ml^. kg^-1. min^-1= 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (work rate)/100 kg

27 ml^. kg^-1. min^-1-7 ml^. kg^-1. min^-1 = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (work

rate)/100 kg-7 ml^. kg^-1. min^-1

20 ml^. kg^-1. min^-1x 100 kg = 1.8 ml^. kg^-1. min^-1 (work rate)/100 kg x 100 kg

2000 ml^. min^-1/1.8= (work rate)

work rate=1111.11 kp^. m^-1. min^-1

work rate = (resistance setting)(flywheel distance)(kpm)

1111.11 kp^. m^-1. min^-1 = (resistance setting)(6 m)(60 kpm)

1111.11 kp^. m^-1. min^-1 = (resistance setting)(360)

1111.11 kp^. m^-1. min^-1/360= (resistance setting)(360)/360

resistance setting = 3.08 kp

5. VO₂ = 3.5 ml^. kg^-1. min^-1 + 3 ml^. kg^-1. min^-1(work rate)/body mass

2.1 L^. min^-1x.60= 1.26 L^. min^-1x 1000=1260 ml^.. min^-1 /53 kg = 23.77 ml^. kg^-1. min^-1

23.77 ml^. kg^-1. min^-1= 3.5 ml^. kg^-1. min^-1 + 3 ml^. kg^-1. min^-1 (work rate)/53 kg

23.77 ml^. kg^-1. min^-1-3.5 ml^. kg^-1. min^-1 = 3.5 ml^. kg^-1. min^-1 + 3 ml^. kg^-1. min^-1 (work

rate)/53 kg-3.5 ml^. kg^-1. min^-1

20.27 ml^. kg^-1. min^-1x 53 kg = 3 ml^. kg^-1. min^-1 (work rate)/53 kg x 53 kg

1074.5 ml^. min^-1/3= (work rate)

work rate=358.16 kp^. m^-1. min^-1

6. 1750 kcal per week x 26 weeks=45500 kcals 45000 kcals/3500 kcals=13 lb

7. VO₂ = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(stepping rate) + 2.4 ml^. kg^-1. min^-1 (stepping rate)(stepping height)

12 in x 0.0254=0.3048 m

VO₂ = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(20) + 2.4 ml^. kg^-1. min^-1 (20)(.3048m)

VO₂ = 3.5 ml^. kg^-1. min^-1 +4 ml^. kg^-1. min^-1 + 14.6304 ml^. kg^-1. min^-1

VO₂ = 22.13 ml^. kg^-1. min^-1

8. VO₂ = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(stepping rate) + 2.4 ml^. kg^-1. min^-1 (stepping rate)(stepping height)

15 ml^. kg^-1. min^-1 = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(24) + 2.4 ml^. kg^-1. min^-1 (24)(stepping height)

Resting-15 ml^. kg^-1. min^-1 - 3.5 ml^. kg^-1. min^-1 = 11.5 ml^. kg^-1. min^-1

11.5 ml^. kg^-1. min^-1 = 4.8 ml^. kg^-1. min^-1 + 2.4 ml^. kg^-1. min^-1 (24)(stepping height)

Vertical-11.5 ml^. kg^-1. min^-1 - 4.8 ml^. kg^-1. min^-1 = 6.7 ml^. kg^-1. min^-1

6.7 ml^. kg^-1. min^-1 = 2.4 ml^. kg^-1. min^-1 (24)(stepping height)

6.7 ml^. kg^-1. min^-1 = 57.6 ml^. kg^-1. min^-1 (stepping height)

6.7 ml^. kg^-1. min^-1 /57.6 ml^. kg^-1. min^-1 =stepping height

stepping height=.11631944 m /.0254= 4.58 in

9. VO₂ = 0.1 ml^. kg^-1. min^-1 (horizontal speed)+1.8 ml^. kg^-1. min^-1(vertical speed)(fractional grade) + 3.5ml^. kg^-1. min^-1

3.2 mph x 26.8 = 85.76 m^.min^-1

VO₂ = 0.1 ml^. kg^-1. min^-1 (87.76 m^. min^-1 )+1.8 ml^. kg^-1. min^-1(87.76 m^. min^-1 )(.12) + 3.5ml^. kg^-1. min^-1

VO₂ = 30.60 ml^. kg^-1. min^-1

10a. VO₂ = 0.2 ml^. kg^-1. min^-1 (horizontal speed) +.9 ml^. kg^-1. min^-1(vertical speed)(fractional grade) + 3.5ml^. kg^-1. min^-1

6 mph x 26.8 = 160.8 m^.min^-1

VO₂ = 0.2 ml^. kg^-1. min^-1 (160.8 m^. min^-1 )+.9 ml^. kg^-1. min^-1(160.8 m^. min^-1 )(.18) + 3.5ml^. kg^-1. min^-1

VO₂ = 61.70 ml^. kg^-1. min^-1/3.5ml^. kg^-1. min^-1

VO₂ =17.53 METs

10b. VO₂ = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (work rate)/body mass

VO₂ = 7 ml^. kg^-1. min^-1 + 1.8 ml^. kg^-1. min^-1 (1200 m^. min^-1)/62 kg)

VO₂ = 41.84 ml^. kg^-1. min^-1/ 3.5ml^. kg^-1. min^-1

VO₂ = 11.95 METs

10c. VO₂ = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(stepping rate) + 2.4 ml^. kg^-1. min^-1 (stepping rate)(stepping height)

12 in x 0.0254=0.3048 m

VO₂ = 3.5 ml^. kg^-1. min^-1 +0.2 ml^. kg^-1. min^-1(50) + 2.4 ml^. kg^-1. min^-1 (50)(.3048)

VO₂ = 50.07 ml^. kg^-1. min^-1 / 3.5ml^. kg^-1. min^-1

VO₂ = 14.30 METs

10d. VO₂ = 0.1 ml^. kg^-1. min^-1 (horizontal speed)+1.8 ml^. kg^-1. min^-1(vertical speed)(fractional grade) + 3.5ml^. kg^-1. min^-1

4 mph x 26.8 =107.2 m^.min^-1

VO₂ = 0.1 ml^. kg^-1. min^-1 (107.2 m^. min^-1 )+1.8 ml^. kg^-1. min^-1(107.2 m^. min^-1)(.05) + 3.5ml^. kg^-1. min^-1

VO₂ = 23.868 ml^. kg^-1. min^-1/3.5ml^. kg^-1. min^-1

VO₂ = 6.8 METs