To solve the problem of calculating the speed of a scooterist who covers a distance of 3 kilometers in 5 minutes, we will follow these steps:
### Step 1: Convert the distance from kilometers to meters.
1 kilometer is equal to 1000 meters. Therefore, to convert 3 kilometers to meters:
\[
\text{Distance in meters} = 3 \, \text{km} \times 1000 \, \text{m/km} = 3000 \, \text{m}
\]
### Step 2: Convert the time from minutes to seconds.
1 minute is equal to 60 seconds. Therefore, to convert 5 minutes to seconds:
\[
\text{Time in seconds} = 5 \, \text{minutes} \times 60 \, \text{s/minute} = 300 \, \text{s}
\]
### Step 3: Calculate the speed in meters per second (m/s).
Speed is defined as distance divided by time. Using the values we calculated:
\[
\text{Speed (m/s)} = \frac{\text{Distance}}{\text{Time}} = \frac{3000 \, \text{m}}{300 \, \text{s}} = 10 \, \text{m/s}
\]
### Step 4: Convert the speed from meters per second to centimeters per second (cm/s).
1 meter is equal to 100 centimeters. Therefore, to convert 10 m/s to cm/s:
\[
\text{Speed (cm/s)} = 10 \, \text{m/s} \times 100 \, \text{cm/m} = 1000 \, \text{cm/s}
\]
### Step 5: Convert the speed from meters per second to kilometers per hour (km/h).
To convert from m/s to km/h, we multiply by \( \frac{18}{5} \):
\[
\text{Speed (km/h)} = 10 \, \text{m/s} \times \frac{18}{5} = 36 \, \text{km/h}
\]
### Final Answers:
(a) Speed in cm/s: **1000 cm/s**
(b) Speed in m/s: **10 m/s**
(c) Speed in km/h: **36 km/h**
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