Velocity Problems worksheet - Free Printable

This worksheet is about velocity, which is a vector quantity — meaning it has both speed and direction. The triangle shown (D = S × T) is the standard formula triangle for distance, speed, and time:

- D = Distance
- S = Speed (or Velocity magnitude)
- T = Time

The formula relationships are:
- Velocity (V) = Distance (D) ÷ Time (T)
- Distance (D) = Velocity (V) × Time (T)
- Time (T) = Distance (D) ÷ Velocity (V)

We must also pay attention to units and include direction where specified.

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Let’s solve each problem step by step.

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1. What is the velocity of a car that traveled a total of 75 kilometers north in 1.5 hours?

- D = 75 km
- T = 1.5 hr
- Direction: north

V = D ÷ T = 75 ÷ 1.5 = 50 km/hr north

✔ Answer: 50 km/hr north

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2. What is the velocity of a plane that traveled 3,000 miles from New York to California in 5 hours?

- D = 3,000 miles
- T = 5 hr
- Direction: west (since NY to CA is generally westward)

V = D ÷ T = 3,000 ÷ 5 = 600 m/hr west

✔ Answer: 600 m/hr west

*(Note: “m” here likely means miles — common shorthand in US contexts)*

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3. John took 45 minutes to bicycle to his grandmother’s house, a total of 4 kilometers, west. What was his velocity?

- D = 4 km
- T = 45 min → convert to hours? No — question asks for km/min (see units given: km/min west)

V = D ÷ T = 4 ÷ 45 ≈ 0.08888... km/min

Rounded to 3 decimals: 0.089 km/min west

✔ Answer: 0.089 km/min west

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4. It took 3.5 hours for a train to travel the distance between two cities at a speed of 120 miles/hour. How many miles lie between the two cities?

- V = 120 m/hr
- T = 3.5 hr
- Find D

D = V × T = 120 × 3.5 = 420 miles

✔ Answer: 420 m

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5. How long would it take for a car to travel a distance of 200 km if it is traveling at a speed of 55 km/hr?

- D = 200 km
- V = 55 km/hr
- Find T

T = D ÷ V = 200 ÷ 55 ≈ 3.6363... hr

Round to 2 decimals: 3.64 hr

✔ Answer: 3.64 hr

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6. A car is traveling at 100 km/hr. How many hours will it take to cover a distance of 750 km?

- V = 100 km/hr
- D = 750 km
- Find T

T = D ÷ V = 750 ÷ 100 = 7.5 hr

✔ Answer: 7.5 hr

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7. A plane traveled for about 2.5 hours at a speed of 1200 km/hr. What distance did it travel?

- V = 1200 km/hr
- T = 2.5 hr
- Find D

D = V × T = 1200 × 2.5 = 3000 km

✔ Answer: 3000 km

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8. A girl is pedaling her bicycle at a speed of .10 kilometers/minute. How far will she travel in 120 minutes?

- V = 0.10 km/min
- T = 120 min
- Find D

D = V × T = 0.10 × 120 = 12 km

✔ Answer: 12 km

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9. An ant carries food at a speed of 1 cm/s. How long will it take the ant to carry a cookie crumb from the kitchen table to the ant hill, a distance of 5000 cm?

- D = 5000 cm
- V = 1 cm/s
- Find T

T = D ÷ V = 5000 ÷ 1 = 5000 sec

✔ Answer: 5000 sec

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10. The water in the Buffalo River flows at an average speed of 5 km/hr. If you and a friend decide to canoe down the river a distance of 16 kilometers, how many hours will it take?

- D = 16 km
- V = 5 km/hr
- Find T

T = D ÷ V = 16 ÷ 5 = 3.2 hr

✔ Answer: 3.2 hr

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## ✔ Final Answers Summary:

1. 50 km/hr north
2. 600 m/hr west
3. 0.089 km/min west
4. 420 m
5. 3.64 hr
6. 7.5 hr
7. 3000 km
8. 12 km
9. 5000 sec
10. 3.2 hr

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📌 Tip for the triangles:
In each triangle, put the variable you’re solving for at the top (D, S, or T), then multiply or divide the other two as needed using the formula triangle.

Example: For velocity (S), cover S → D over T → so S = D/T.

You’ve got this! 🚗✈️🚲