Speed and Velocity Worksheet Answer Key | Calculating speed, Speed ... - Free Printable

Problem: Solving the Velocity and Speed Problems

The worksheet involves calculating velocity, speed, distance, and time using the formulas:
- Speed = Distance / Time
- Velocity = Distance / Time (in a specific direction)

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?

#### Solution:
- Distance = 75 km
- Time = 1.5 hours
- Velocity = Distance / Time = 75 km / 1.5 hours = 50 km/hr (north)

#### Answer:
$$
\boxed{50 \text{ km/hr}}
$$

---

2. What is the velocity of a plane that traveled 3,000 miles from New York to California in 5.0 hours?

#### Solution:
- Distance = 3,000 miles
- Time = 5.0 hours
- Velocity = Distance / Time = 3,000 miles / 5.0 hours = 600 miles/hr

#### Answer:
$$
\boxed{600 \text{ miles/hr}}
$$

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3. John took 45 minutes to bicycle to his grandmother’s house, a total of four kilometers. What was his velocity in km/hr?

#### Solution:
- Distance = 4 km
- Time = 45 minutes = 45/60 hours = 0.75 hours
- Velocity = Distance / Time = 4 km / 0.75 hours = 5.33 km/hr

#### Answer:
$$
\boxed{5.33 \text{ km/hr}}
$$

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

#### Solution:
- Velocity = 120 miles/hr
- Time = 3.5 hours
- Distance = Velocity × Time = 120 miles/hr × 3.5 hours = 420 miles

#### Answer:
$$
\boxed{420 \text{ miles}}
$$

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

#### Solution:
- Distance = 200 km
- Velocity = 55 km/hr
- Time = Distance / Velocity = 200 km / 55 km/hr ≈ 3.64 hours

#### Answer:
$$
\boxed{3.64 \text{ hours}}
$$

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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?

#### Solution:
- Distance = 750 km
- Velocity = 100 km/hr
- Time = Distance / Velocity = 750 km / 100 km/hr = 7.5 hours

#### Answer:
$$
\boxed{7.5 \text{ hours}}
$$

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

#### Solution:
- Velocity = 1200 km/hr
- Time = 2.5 hours
- Distance = Velocity × Time = 1200 km/hr × 2.5 hours = 3000 km

#### Answer:
$$
\boxed{3000 \text{ km}}
$$

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8. A girl is pedaling her bicycle at a velocity of 0.10 km/min. How far will she travel in two hours?

#### Solution:
- Velocity = 0.10 km/min
- Time = 2 hours = 2 × 60 minutes = 120 minutes
- Distance = Velocity × Time = 0.10 km/min × 120 minutes = 12 km

#### Answer:
$$
\boxed{12 \text{ km}}
$$

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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 50 m? Express your answer in seconds, minutes, and hours.

#### Solution:
- Speed = 1 cm/s
- Distance = 50 m = 50 × 100 cm = 5000 cm
- Time = Distance / Speed = 5000 cm / 1 cm/s = 5000 seconds

Convert seconds to minutes and hours:
- Minutes = 5000 seconds / 60 = 83.33 minutes
- Hours = 5000 seconds / 3600 = 1.39 hours

#### Answer:
$$
\boxed{5000 \text{ seconds}, 83.33 \text{ minutes}, 1.39 \text{ hours}}
$$

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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 and minutes will it take?

#### Solution:
- Speed = 5 km/hr
- Distance = 16 km
- Time = Distance / Speed = 16 km / 5 km/hr = 3.2 hours

Convert hours to hours and minutes:
- Hours = 3
- Minutes = 0.2 × 60 = 12 minutes

#### Answer:
$$
\boxed{3 \text{ hours and } 12 \text{ minutes}}
$$

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Final Answers:

1. $ \boxed{50 \text{ km/hr}} $
2. $ \boxed{600 \text{ miles/hr}} $
3. $ \boxed{5.33 \text{ km/hr}} $
4. $ \boxed{420 \text{ miles}} $
5. $ \boxed{3.64 \text{ hours}} $
6. $ \boxed{7.5 \text{ hours}} $
7. $ \boxed{3000 \text{ km}} $
8. $ \boxed{12 \text{ km}} $
9. $ \boxed{5000 \text{ seconds}, 83.33 \text{ minutes}, 1.39 \text{ hours}} $
10. $ \boxed{3 \text{ hours and } 12 \text{ minutes}} $