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Velocity 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: Time
- Displacement (Δx): 170 km
- Average velocity (v): 90 km/h
- Show time in: Milliseconds (ms)
Find: Time
Answer
2.
Problem 2.
- Solve for: Displacement
- Time taken (t): 1.1 h
- Average velocity (v): 65 km/h
- Show displacement in: Feet (ft)
Find: Displacement
Answer
3.
Problem 3.
- Solve for: Displacement
- Time taken (t): 1.3 h
- Average velocity (v): 70 km/h
- Show displacement in: Kilometers (km)
Find: Displacement
Answer
4.
Problem 4.
- Solve for: Final velocity (v = u + at)
- Initial velocity (u): 6 m/s
- Acceleration (a): 2.2 m/s²
- Time (t): 6 s
- Show velocity in: Meters per second (m/s)
Find: Final velocity
Answer
5.
Problem 5.
- Solve for: Time
- Displacement (Δx): 100 km
- Average velocity (v): 95 km/h
- Show time in: Milliseconds (ms)
Find: Time
Answer
6.
Problem 6.
- Solve for: Displacement
- Time taken (t): 2.2 h
- Average velocity (v): 92 km/h
- Show displacement in: Yards (yd)
Find: Displacement
Answer
7.
Problem 7.
- Solve for: Final velocity (v = u + at)
- Initial velocity (u): 7 m/s
- Acceleration (a): 2.8 m/s²
- Time (t): 8 s
- Show velocity in: Kilometers per hour (km/h)
Find: Final velocity
Answer
8.
Problem 8.
- Solve for: Displacement
- Time taken (t): 1.6 h
- Average velocity (v): 95 km/h
- Show displacement in: Kilometers (km)
Find: Displacement
Answer
9.
Problem 9.
- Solve for: Displacement
- Time taken (t): 1.3 h
- Average velocity (v): 56 km/h
- Show displacement in: Nautical miles (nmi)
Find: Displacement
Answer
10.
Problem 10.
- Solve for: Displacement
- Time taken (t): 1.4 h
- Average velocity (v): 75 km/h
- Show displacement in: Yards (yd)
Find: Displacement
Answer

Answer key: Velocity worksheet

1. Time: 6,800,000 ms
1. Change displacement to m, the standard unit the formula uses (1 km = 1,000 m)
  $170 km \times 1,000$ $= 170,000 m$
2. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $90 km/h \times 0.277777777778$ $= 25 m/s$
3. Divide how far it moved by the average velocity, to find how long it took
  $\frac{170,000}{25}$ $= 6,800 s$
4. Change the answer to ms, the unit you picked: divide by 0.001
  $\frac{6,800}{0.001}$ $= 6,800,000 ms$
2. Displacement: 234,580.05 ft
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $65 km/h \times 0.277777777778$ $= 18.055556 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $1.1 h \times 3,600$ $= 3,960 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $18.055556 \times 3,960$ $= 71,500 m$
4. Change the answer to ft, the unit you picked: divide by 0.3048
  $\frac{71,500}{0.3048}$ $= 234,580.052493 ft$
3. Displacement: 91 km
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $70 km/h \times 0.277777777778$ $= 19.444444 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $1.3 h \times 3,600$ $= 4,680 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $19.444444 \times 4,680$ $= 91,000 m$
4. Change the answer to km, the unit you picked: divide by 1,000
  $\frac{91,000}{1,000}$ $= 91 km$
4. Final velocity: 19.2 m/s
1. Find the final velocity (v). Start from the starting velocity (u) and add the acceleration (a) times the time (t)
  $6 + 2.2 \times 6$ $= 19.2 m/s$
2. Find how far it moved in that time (s): the starting velocity × the time, plus half the acceleration × the time squared
  $6 \times 6 + 0.5 \times 2.2 \times 6^{2}$ $= 75.6 m$
3. With steady acceleration, the average velocity is halfway between the starting and final velocity
  $\frac{6 + 19.2}{2}$ $= 12.6 m/s$
4. Find how much the velocity changed (Δv): the final velocity minus the starting velocity
  $19.2 - 6$ $= 13.2 m/s$
5. Time: 3,789,473.68 ms
1. Change displacement to m, the standard unit the formula uses (1 km = 1,000 m)
  $100 km \times 1,000$ $= 100,000 m$
2. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $95 km/h \times 0.277777777778$ $= 26.388889 m/s$
3. Divide how far it moved by the average velocity, to find how long it took
  $\frac{100,000}{26.388889}$ $= 3,789.473684 s$
4. Change the answer to ms, the unit you picked: divide by 0.001
  $\frac{3,789.473684}{0.001}$ $= 3,789,473.684211 ms$
6. Displacement: 221,347.33 yd
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $92 km/h \times 0.277777777778$ $= 25.555556 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $2.2 h \times 3,600$ $= 7,920 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $25.555556 \times 7,920$ $= 202,400 m$
4. Change the answer to yd, the unit you picked: divide by 0.9144
  $\frac{202,400}{0.9144}$ $= 221,347.331584 yd$
7. Final velocity: 105.84 km/h
1. Find the final velocity (v). Start from the starting velocity (u) and add the acceleration (a) times the time (t)
  $7 + 2.8 \times 8$ $= 29.4 m/s$
2. Find how far it moved in that time (s): the starting velocity × the time, plus half the acceleration × the time squared
  $7 \times 8 + 0.5 \times 2.8 \times 8^{2}$ $= 145.6 m$
3. With steady acceleration, the average velocity is halfway between the starting and final velocity
  $\frac{7 + 29.4}{2}$ $= 18.2 m/s$
4. Find how much the velocity changed (Δv): the final velocity minus the starting velocity
  $29.4 - 7$ $= 22.4 m/s$
5. Change the answer to km/h, the unit you picked: divide by 0.277777777778
  $\frac{29.4}{0.277777777778}$ $= 105.84 km/h$
8. Displacement: 152 km
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $95 km/h \times 0.277777777778$ $= 26.388889 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $1.6 h \times 3,600$ $= 5,760 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $26.388889 \times 5,760$ $= 152,000 m$
4. Change the answer to km, the unit you picked: divide by 1,000
  $\frac{152,000}{1,000}$ $= 152 km$
9. Displacement: 39.31 nmi
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $56 km/h \times 0.277777777778$ $= 15.555556 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $1.3 h \times 3,600$ $= 4,680 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $15.555556 \times 4,680$ $= 72,800 m$
4. Change the answer to nmi, the unit you picked: divide by 1,852
  $\frac{72,800}{1,852}$ $= 39.308855 nmi$
10. Displacement: 114,829.4 yd
1. Change velocity to m/s, the standard unit the formula uses (1 km/h = 0.277777777778 m/s)
  $75 km/h \times 0.277777777778$ $= 20.833333 m/s$
2. Change time to s, the standard unit the formula uses (1 h = 3,600 s)
  $1.4 h \times 3,600$ $= 5,040 s$
3. Multiply the average velocity by the time, to find how far it moved (the displacement)
  $20.833333 \times 5,040$ $= 105,000 m$
4. Change the answer to yd, the unit you picked: divide by 0.9144
  $\frac{105,000}{0.9144}$ $= 114,829.396325 yd$