Question

determining speed (velocity)
speed is a measure of how fast an object is moving or traveling. velocity is a measure of how fast an object is traveling in a certain direction. both speed and velocity include the distance traveled compared to the amount of time taken to cover this distance.
speed = \frac{distance}{time} velocity = \frac{distance}{time} in a specific direction
answer the following questions.

1. what is the velocity of a car that traveled a total of 75 kilometers north in 1.5 hours?
2. what is the velocity of a plane that traveled 3,000 miles from new york to california in 5.0 hours?
3. john took 45 minutes to bicycle to his grandmother’s house, a total of four kilometers. what was his velocity in km/hr?
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?
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?
6. a car is traveling at 100 km/hr. how many hours will it take to cover a distance of 750 km?
7. a plane traveled for about 2.5 hours at a velocity of 1200 km/hr. what distance did it travel?
8. a girl is pedaling her bicycle at a velocity of 0.10 km/min. how far will she travel in two hours?
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.
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?

Explanation:

Step1: Velocity formula

Velocity = distance/time (with direction)

Step2: Calculate speed

$75 \, \text{km} / 1.5 \, \text{hr} = 50 \, \text{km/hr}$

Step3: Add direction

North

Step1: Velocity formula

Velocity = distance/time (with direction)

Step2: Calculate speed

$3000 \, \text{miles} / 5.0 \, \text{hr} = 600 \, \text{miles/hr}$

Step3: Add direction

West (New York to California)

Step1: Convert time to hours

$45 \, \text{min} = 45/60 = 0.75 \, \text{hr}$

Step2: Velocity formula

Velocity = distance/time

Step3: Calculate

$4 \, \text{km} / 0.75 \, \text{hr} \approx 5.33 \, \text{km/hr}$

Step1: Distance formula

Distance = velocity×time

Step2: Calculate

$120 \, \text{miles/hr} × 3.5 \, \text{hr} = 420 \, \text{miles}$

Step1: Time formula

Time = distance/velocity

Step2: Calculate

$200 \, \text{km} / 55 \, \text{km/hr} \approx 3.64 \, \text{hr}$

Step1: Time formula

Time = distance/velocity

Step2: Calculate

$750 \, \text{km} / 100 \, \text{km/hr} = 7.5 \, \text{hr}$

Step1: Distance formula

Distance = velocity×time

Step2: Calculate

$1200 \, \text{km/hr} × 2.5 \, \text{hr} = 3000 \, \text{km}$

Step1: Convert time to minutes

$2 \, \text{hr} = 2×60 = 120 \, \text{min}$

Step2: Distance formula

Distance = velocity×time

Step3: Calculate

$0.10 \, \text{km/min} × 120 \, \text{min} = 12 \, \text{km}$

Step1: Convert distance to cm

$50 \, \text{m} = 50×100 = 5000 \, \text{cm}$

Step2: Time in seconds

$5000 \, \text{cm} / 1 \, \text{cm/s} = 5000 \, \text{s}$

Step3: Convert to minutes

$5000 \, \text{s} / 60 ≈ 83.33 \, \text{min}$

Step4: Convert to hours

$83.33 \, \text{min} / 60 ≈ 1.39 \, \text{hr}$

Step1: Time formula

Time = distance/speed

Step2: Calculate hours

$16 \, \text{km} / 5 \, \text{km/hr} = 3.2 \, \text{hr}$

Step3: Convert 0.2 hr to minutes

$0.2×60 = 12 \, \text{min}$

Answer:

1. 50 km/hr north
2. 600 miles/hr west
3. Approximately 5.33 km/hr
4. 420 miles
5. Approximately 3.64 hours
6. 7.5 hours
7. 3000 km
8. 12 km
9. 5000 seconds, approximately 83.33 minutes, approximately 1.39 hours
10. 3 hours and 12 minutes