Question

1. sabiendo que nada 8000 metros en 15 segundos calcula la velocidad.
2. un ciclista en una carrera recorre 12,000 m en 15 minutos. calcula la velocidad.
3. un avión despega del aeropuerto recorriendo una distancia de 1,000,000 de metros en 12 horas. calcula la velocidad y expresa en km/h.
4. un perro en una carrera recorre una distancia de 95 m en 5 segundos. calcula la velocidad y expresa el resultado en km/h.
5. un motociclista viaja una distancia de 600 km en 20 minutos. calcula la velocidad.

Explanation:

Step1: Recall velocity formula

Velocity $v=\frac{d}{t}$, where $d$ is distance and $t$ is time. We need to make sure units are consistent.

Step2: First problem - convert units and calculate

1. Given $d = 8000$ m and $t=15$ s. First convert distance to km: $8000$ m $= 8$ km, and time to hours. Since $1$ hour $= 3600$ s, $t=\frac{15}{3600}=\frac{1}{240}$ h. Then $v=\frac{d}{t}=\frac{8}{\frac{1}{240}} = 1920$ km/h.

Step3: Second problem - convert units and calculate

1. Given $d = 12000$ m and $t = 15$ min. Convert distance to km: $12000$ m $= 12$ km, and time to hours. Since $1$ hour $= 60$ min, $t=\frac{15}{60}=0.25$ h. Then $v=\frac{d}{t}=\frac{12}{0.25}=48$ km/h.

Step4: Third problem - calculate velocity

1. Given $d = 1000$ km and $t = 12$ h. Using $v=\frac{d}{t}$, we get $v=\frac{1000}{12}=\frac{250}{3}\approx83.33$ km/h.

Step5: Fourth problem - convert units and calculate

1. Given $d = 95$ m and $t = 5$ s. Convert distance to km: $95$ m $=0.095$ km, and time to hours. $t=\frac{5}{3600}$ h. Then $v=\frac{d}{t}=\frac{0.095}{\frac{5}{3600}}=0.095\times\frac{3600}{5}=68.4$ km/h.

Step6: Fifth problem - convert units and calculate

1. Given $d = 600$ km and $t = 20$ min. Convert time to hours: $t=\frac{20}{60}=\frac{1}{3}$ h. Then $v=\frac{d}{t}=\frac{600}{\frac{1}{3}} = 1800$ km/h.

Answer:

First velocity: 1920 km/h; Second velocity: 48 km/h; Third velocity: $\frac{250}{3}\approx83.33$ km/h; Fourth velocity: 68.4 km/h; Fifth velocity: 1800 km/h