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Kinetic Energy worksheet

Grades 8–9 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Mass
- Speed (v): 140 km/h
- Kinetic energy (KE): 550 kJ
- Show mass in: Kilograms (kg)
Find: Mass
Answer
2.
Problem 2.
- Solve for: Mass
- Speed (v): 76 km/h
- Kinetic energy (KE): 400 kJ
- Show mass in: Grams (g)
Find: Mass
Answer
3.
Problem 3.
- Solve for: Kinetic energy
- Mass (m): 1,300 kg
- Speed (v): 90 km/h
- Show energy in: Joules (J)
Find: Kinetic energy
Answer
4.
Problem 4.
- Solve for: Speed
- Mass (m): 1,800 kg
- Kinetic energy (KE): 450 kJ
- Show speed in: Meters per second (m/s)
Find: Speed
Answer
5.
Problem 5.
- Solve for: Mass
- Speed (v): 100 km/h
- Kinetic energy (KE): 400 kJ
- Show mass in: Kilograms (kg)
Find: Mass
Answer
6.
Problem 6.
- Solve for: Kinetic energy
- Mass (m): 1,500 kg
- Speed (v): 140 km/h
- Show energy in: Kilowatt-hours (kWh)
Find: Kinetic energy
Answer
7.
Problem 7.
- Solve for: Speed
- Mass (m): 1,250 kg
- Kinetic energy (KE): 650 kJ
- Show speed in: Feet per second (ft/s)
Find: Speed
Answer
8.
Problem 8.
- Solve for: Kinetic energy
- Mass (m): 1,850 kg
- Speed (v): 80 km/h
- Show energy in: Kilocalories (kcal)
Find: Kinetic energy
Answer
9.
Problem 9.
- Solve for: Mass
- Speed (v): 100 km/h
- Kinetic energy (KE): 375 kJ
- Show mass in: Pounds (lb)
Find: Mass
Answer
10.
Problem 10.
- Solve for: Kinetic energy
- Mass (m): 1,525 kg
- Speed (v): 65 km/h
- Show energy in: Joules (J)
Find: Kinetic energy
Answer

Answer key: Kinetic Energy worksheet

1. Mass: 727.35 kg
1. Convert energy to J (1 kJ = 1,000 J)
  $550 kJ \times 1,000$ $= 550,000 J$
2. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $140 km/h \times 0.277777777778$ $= 38.888889 m/s$
3. Work the energy formula backwards to find the mass: double the energy, then divide by the speed squared
  $\frac{2 \times 550,000}{{38.888889}^{2}}$ $= 727.346939 kg$
2. Mass: 1,795,013.85 g
1. Convert energy to J (1 kJ = 1,000 J)
  $400 kJ \times 1,000$ $= 400,000 J$
2. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $76 km/h \times 0.277777777778$ $= 21.111111 m/s$
3. Work the energy formula backwards to find the mass: double the energy, then divide by the speed squared
  $\frac{2 \times 400,000}{{21.111111}^{2}}$ $= 1,795.01385 kg$
4. Convert to g: divide by 0.001
  $\frac{1,795.01385}{0.001}$ $= 1,795,013.850416 g$
3. Kinetic energy: 406,250 J
1. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $90 km/h \times 0.277777777778$ $= 25 m/s$
2. Multiply half the mass by the speed squared; squaring is why speed matters so much more than mass
  $\frac{1}{2} \times 1,300 \times 25^{2}$ $= 406,250 J$
4. Speed: 22.36 m/s
1. Convert energy to J (1 kJ = 1,000 J)
  $450 kJ \times 1,000$ $= 450,000 J$
2. Work the energy formula backwards to find the speed: double the energy, divide by the mass, then take the square root
  $\sqrt{\frac{2 \times 450,000}{1,800}}$ $= 22.36068 m/s$
5. Mass: 1,036.8 kg
1. Convert energy to J (1 kJ = 1,000 J)
  $400 kJ \times 1,000$ $= 400,000 J$
2. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $100 km/h \times 0.277777777778$ $= 27.777778 m/s$
3. Work the energy formula backwards to find the mass: double the energy, then divide by the speed squared
  $\frac{2 \times 400,000}{{27.777778}^{2}}$ $= 1,036.8 kg$
6. Kinetic energy: 0.32 kWh
1. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $140 km/h \times 0.277777777778$ $= 38.888889 m/s$
2. Multiply half the mass by the speed squared; squaring is why speed matters so much more than mass
  $\frac{1}{2} \times 1,500 \times {38.888889}^{2}$ $= 1,134,259.259259 J$
3. Convert to kWh: divide by 3,600,000
  $\frac{1,134,259.259259}{3,600,000}$ $= 0.315072 kWh$
7. Speed: 105.8 ft/s
1. Convert energy to J (1 kJ = 1,000 J)
  $650 kJ \times 1,000$ $= 650,000 J$
2. Work the energy formula backwards to find the speed: double the energy, divide by the mass, then take the square root
  $\sqrt{\frac{2 \times 650,000}{1,250}}$ $= 32.249031 m/s$
3. Convert to ft/s: divide by 0.3048
  $\frac{32.249031}{0.3048}$ $= 105.803907 ft/s$
8. Kinetic energy: 109.18 kcal
1. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $80 km/h \times 0.277777777778$ $= 22.222222 m/s$
2. Multiply half the mass by the speed squared; squaring is why speed matters so much more than mass
  $\frac{1}{2} \times 1,850 \times {22.222222}^{2}$ $= 456,790.123457 J$
3. Convert to kcal: divide by 4,184
  $\frac{456,790.123457}{4,184}$ $= 109.17546 kcal$
9. Mass: 2,142.89 lb
1. Convert energy to J (1 kJ = 1,000 J)
  $375 kJ \times 1,000$ $= 375,000 J$
2. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $100 km/h \times 0.277777777778$ $= 27.777778 m/s$
3. Work the energy formula backwards to find the mass: double the energy, then divide by the speed squared
  $\frac{2 \times 375,000}{{27.777778}^{2}}$ $= 972 kg$
4. Convert to lb: divide by 0.45359237
  $\frac{972}{0.45359237}$ $= 2,142.893188 lb$
10. Kinetic energy: 248,577.35 J
1. Convert speed to m/s (1 km/h = 0.277777777778 m/s)
  $65 km/h \times 0.277777777778$ $= 18.055556 m/s$
2. Multiply half the mass by the speed squared; squaring is why speed matters so much more than mass
  $\frac{1}{2} \times 1,525 \times {18.055556}^{2}$ $= 248,577.353395 J$