Question

use the formula $v = \frac{d}{t}$. show your work.

1. a car travels 120 km in 2 hours. what is its average velocity?
2. a runner sprints at 8 m/s for 12 seconds. how far does she run?
3. a bicycle covers 45 km in 3 hours. what is its velocity?
4. a person walks 900 m in 15 minutes. what is their average speed in m/s?
5. a bus moves at 60 km/h for 2.5 hours. how far does it go?
6. a train covers 250 km at 100 km/h. how long does the trip take?
7. a skateboarder moves at 3 m/s for 40 seconds. what distance is traveled?
8. a swimmer goes 1,500 m in 25 minutes. what is their average velocity?
9. a car moves 75 km in 1.5 hours. what is its velocity?
10. a person jogging at 2.5 m/s covers 5,000 m. how long do they run?

Explanation:

Step1: Identify the formula

The formula for velocity is $v=\frac{d}{t}$, where $v$ is velocity, $d$ is distance and $t$ is time. We can also re - arrange it as $d = v\times t$ and $t=\frac{d}{v}$.

Step2: Solve problem 1

Given $d = 120$ km and $t = 2$ h. Using $v=\frac{d}{t}$, we have $v=\frac{120}{2}=60$ km/h.

Step3: Solve problem 2

Given $v = 8$ m/s and $t = 12$ s. Using $d=v\times t$, we get $d=8\times12 = 96$ m.

Step4: Solve problem 3

Given $d = 45$ km and $t = 3$ h. Using $v=\frac{d}{t}$, we have $v=\frac{45}{3}=15$ km/h.

Step5: Solve problem 4

First convert $t = 15$ min to seconds. Since $1$ min=$60$ s, $t=15\times60 = 900$ s and $d = 900$ m. Using $v=\frac{d}{t}$, we get $v=\frac{900}{900}=1$ m/s.

Step6: Solve problem 5

Given $v = 60$ km/h and $t = 2.5$ h. Using $d=v\times t$, we have $d=60\times2.5 = 150$ km.

Step7: Solve problem 6

Given $d = 250$ km and $v = 100$ km/h. Using $t=\frac{d}{v}$, we get $t=\frac{250}{100}=2.5$ h.

Step8: Solve problem 7

Given $v = 3$ m/s and $t = 40$ s. Using $d=v\times t$, we have $d=3\times40 = 120$ m.

Step9: Solve problem 8

First convert $t = 25$ min to seconds. $t=25\times60=1500$ s and $d = 1500$ m. Using $v=\frac{d}{t}$, we get $v=\frac{1500}{1500}=1$ m/s.

Step10: Solve problem 10

Given $v = 2.5$ m/s and $d = 5000$ m. Using $t=\frac{d}{v}$, we have $t=\frac{5000}{2.5}=2000$ s.

Answer:

1. 60 km/h
2. 96 m
3. 15 km/h
4. 1 m/s
5. 150 km
6. 2.5 h
7. 120 m
8. 1 m/s
9. 50 km/h (since $v=\frac{75}{1.5}=50$ km/h)
10. 2000 s