Calculating Athlete's Speed

This question asks us to determine the speed of an athlete who runs a specific distance in a given time. We are provided with the distance in meters and the time in seconds, but the required speed unit is kilometers per hour (km/h). Therefore, we need to perform unit conversions before calculating the speed.

Let's identify the given values:

• Distance = 800 meters (m)
• Time = 96 seconds (s)

To find the speed in km/h, we first need to convert the distance from meters to kilometers and the time from seconds to hours.

Converting Units for Speed Calculation

Distance Conversion:

There are 1000 meters in 1 kilometer. To convert meters to kilometers, we divide by 1000.

Distance in km = $\frac{800 \text{ m}}{1000 \text{ m/km}} = 0.8 \text{ km}$

Time Conversion:

There are 60 seconds in 1 minute and 60 minutes in 1 hour. So, there are $60 \times 60 = 3600$ seconds in 1 hour. To convert seconds to hours, we divide by 3600.

Time in hours = $\frac{96 \text{ seconds}}{3600 \text{ seconds/hour}}$

We can simplify the fraction $\frac{96}{3600}$. Both are divisible by 12:

$\frac{96 \div 12}{3600 \div 12} = \frac{8}{300}$

Both are divisible by 4:

$\frac{8 \div 4}{300 \div 4} = \frac{2}{75}$

So, Time in hours = $\frac{2}{75}$ hours.

Calculating Speed in km/h

The formula for speed is:

Speed = $\frac{\text{Distance}}{\text{Time}}$

Now, we use the converted values for distance and time:

Speed = $\frac{0.8 \text{ km}}{\frac{2}{75} \text{ hours}}$

To divide by a fraction, we multiply by its reciprocal:

Speed = $0.8 \times \frac{75}{2} \text{ km/h}$

Convert 0.8 to a fraction: $0.8 = \frac{8}{10} = \frac{4}{5}$

Speed = $\frac{4}{5} \times \frac{75}{2} \text{ km/h}$

We can simplify before multiplying:

Speed = $\frac{4}{2} \times \frac{75}{5} \text{ km/h}$

Speed = $2 \times 15 \text{ km/h}$

Speed = $30 \text{ km/h}$

Thus, the athlete's speed is 30 km/h.

Comparing with Options

Let's look at the given options:

• 1. 30 km / h
• 2. 20 km / h
• 3. 40 km / h
• 4. 25 km / h

Our calculated speed is 30 km/h, which matches the first option.

Revision Table: Speed Calculation Concepts

Additional Information: Understanding Speed Units

Speed is a measure of how quickly an object moves over a certain distance. It is typically expressed in units of distance per unit of time.

• Meters per second (m/s): This is the standard SI unit for speed. It measures the distance in meters covered in one second.
• Kilometers per hour (km/h): This unit is commonly used for vehicle speeds or longer distances. It measures the distance in kilometers covered in one hour.
• Miles per hour (mph): This unit is used in some countries, like the United States and the United Kingdom.

Being able to convert between different units of speed is important in physics and everyday calculations. For example, converting m/s to km/h involves converting meters to kilometers and seconds to hours simultaneously, which simplifies to multiplying by $\frac{18}{5}$. Conversely, converting km/h to m/s involves multiplying by $\frac{5}{18}$.

In this problem, converting the given units (m and s) to the required units (km and h) was the crucial first step before applying the speed formula.