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Acceleration worksheet

Grades 9–10 · CCSS HSA.CED.A.4

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

1.
Problem 1.
- Formula: Force and mass: a = F ÷ m
- Solve for: Acceleration
- Net force (F): 4,000 N
- Mass (m): 1,500 kg
- Show acceleration in: Feet per second squared (ft/s²)
Find: Acceleration
Answer
2.
Problem 2.
- Formula: Force and mass: a = F ÷ m
- Solve for: Acceleration
- Net force (F): 2,400 N
- Mass (m): 1,175 kg
- Show acceleration in: Feet per second squared (ft/s²)
Find: Acceleration
Answer
3.
Problem 3.
- Formula: Velocity change: a = (v − u) ÷ t
- Solve for: Final velocity
- Initial velocity (u): 9 m/s
- Time taken (t): 8 s
- Acceleration (a): 3.2 m/s²
- Show velocity in: Miles per hour (mph)
Find: Final velocity
Answer
4.
Problem 4.
- Formula: Distance: v² = u² + 2as
- Solve for: Acceleration
- Initial velocity (u): 8 m/s
- Final velocity (v): 25 m/s
- Distance travelled (s): 180 m
- Show acceleration in: Meters per second squared (m/s²)
Find: Acceleration
Answer
5.
Problem 5.
- Formula: Distance: v² = u² + 2as
- Solve for: Final velocity
- Initial velocity (u): 14 m/s
- Distance travelled (s): 240 m
- Acceleration (a): 2.2 m/s²
- Show velocity in: Kilometers per hour (km/h)
Find: Final velocity
Answer
6.
Problem 6.
- Formula: Force and mass: a = F ÷ m
- Solve for: Mass
- Net force (F): 3,400 N
- Acceleration (a): 2.5 m/s²
- Show mass in: Pounds (lb)
Find: Mass
Answer
7.
Problem 7.
- Formula: Force and mass: a = F ÷ m
- Solve for: Acceleration
- Net force (F): 2,500 N
- Mass (m): 1,100 kg
- Show acceleration in: Feet per second squared (ft/s²)
Find: Acceleration
Answer
8.
Problem 8.
- Formula: Distance: v² = u² + 2as
- Solve for: Final velocity
- Initial velocity (u): 10 m/s
- Distance travelled (s): 110 m
- Acceleration (a): 2.4 m/s²
- Show velocity in: Meters per second (m/s)
Find: Final velocity
Answer
9.
Problem 9.
- Formula: Velocity change: a = (v − u) ÷ t
- Solve for: Time
- Initial velocity (u): 15 m/s
- Final velocity (v): 26 m/s
- Acceleration (a): 2.6 m/s²
- Show time in: Seconds (s)
Find: Time
Answer
10.
Problem 10.
- Formula: Distance: v² = u² + 2as
- Solve for: Distance
- Initial velocity (u): 7 m/s
- Final velocity (v): 32 m/s
- Acceleration (a): 3.4 m/s²
- Show distance in: Miles (mi)
Find: Distance
Answer

Answer key: Acceleration worksheet

1. Acceleration: 8.75 ft/s²
1. Newton's second law says force = mass × acceleration, so divide the force by the mass: a = F ÷ m
  $\frac{4,000}{1,500}$ $= 2.666667 m/s²$
2. Change the answer to ft/s², the unit you picked: divide by 0.3048
  $\frac{2.666667}{0.3048}$ $= 8.748906 ft/s²$
2. Acceleration: 6.7 ft/s²
1. Newton's second law says force = mass × acceleration, so divide the force by the mass: a = F ÷ m
  $\frac{2,400}{1,175}$ $= 2.042553 m/s²$
2. Change the answer to ft/s², the unit you picked: divide by 0.3048
  $\frac{2.042553}{0.3048}$ $= 6.70129 ft/s²$
3. Final velocity: 77.4 mph
1. The final velocity is the starting velocity plus the speed gained over the time: v = u + a × t
  $9 + 3.2 \times 8$ $= 34.6 m/s$
2. Change the answer to mph, the unit you picked: divide by 0.44704
  $\frac{34.6}{0.44704}$ $= 77.397996 mph$
4. Acceleration: 1.56 m/s²
1. Use the formula linking speed and distance, v² = u² + 2as, rearranged to find acceleration: a = (v² − u²) ÷ (2s)
  $\frac{25^{2} - 8^{2}}{2 \times 180}$ $= 1.558333 m/s²$
5. Final velocity: 127.38 km/h
1. Find the final velocity squared from the speed-and-distance formula: v² = u² + 2as
  $14^{2} + 2 \times 2.2 \times 240$ $= 1,252 m²/s²$
2. Take the square root to get the velocity. The positive answer is the speed in the direction of travel
  $\sqrt{1,252}$ $= 35.383612 m/s$
3. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{35.383612}{0.277777777778}$ $= 127.381003 km/h$
6. Mass: 2,998.29 lb
1. Turn Newton's second law around to find the mass: m = F ÷ a
  $\frac{3,400}{2.5}$ $= 1,360 kg$
2. Change the answer to lb, the unit you picked: divide by 0.45359237
  $\frac{1,360}{0.45359237}$ $= 2,998.286766 lb$
7. Acceleration: 7.46 ft/s²
1. Newton's second law says force = mass × acceleration, so divide the force by the mass: a = F ÷ m
  $\frac{2,500}{1,100}$ $= 2.272727 m/s²$
2. Change the answer to ft/s², the unit you picked: divide by 0.3048
  $\frac{2.272727}{0.3048}$ $= 7.456454 ft/s²$
8. Final velocity: 25.06 m/s
1. Find the final velocity squared from the speed-and-distance formula: v² = u² + 2as
  $10^{2} + 2 \times 2.4 \times 110$ $= 628 m²/s²$
2. Take the square root to get the velocity. The positive answer is the speed in the direction of travel
  $\sqrt{628}$ $= 25.059928 m/s$
9. Time: 4.23 s
1. The time is the change in velocity divided by how fast it changes: t = (v − u) ÷ a
  $\frac{26 - 15}{2.6}$ $= 4.230769 s$
10. Distance: 0.09 mi
1. Use the formula linking speed and distance, v² = u² + 2as, rearranged to find distance: s = (v² − u²) ÷ (2a)
  $\frac{32^{2} - 7^{2}}{2 \times 3.4}$ $= 143.382353 m$
2. Change the answer to mi, the unit you picked: divide by 1,609.344
  $\frac{143.382353}{1,609.344}$ $= 0.089094 mi$