Certainly! Let's calculate the speed of the cyclist in different units step-by-step.
### Given:
- Distance: 6 kilometers
- Time: 10 minutes
### Step-by-Step Solution:
#### (i) Speed in centimeters per second (cm/sec):
1. Convert the distance to centimeters:
- Since 1 kilometer = 100,000 centimeters,
- Distance = 6 km × 100,000 cm/km = 600,000 cm
2. Convert the time to seconds:
- Since 1 minute = 60 seconds,
- Time = 10 minutes × 60 seconds/minute = 600 seconds
3. Calculate the speed:
- Speed = Distance / Time
- Speed = 600,000 cm / 600 s = 1,000 cm/sec
So, the speed of the cyclist is 1,000 centimeters per second.
#### (ii) Speed in meters per second (m/sec):
1. Convert the distance to meters:
- Since 1 kilometer = 1,000 meters,
- Distance = 6 km × 1,000 m/km = 6,000 meters
2. Use the time in seconds (which we already converted above):
- Time = 600 seconds
3. Calculate the speed:
- Speed = Distance / Time
- Speed = 6,000 meters / 600 seconds = 10 m/sec
So, the speed of the cyclist is 10 meters per second.
#### (iii) Speed in kilometers per hour (km/hr):
1. Use the given distance in kilometers:
- Distance = 6 km
2. Convert the time to hours:
- Since 1 hour = 60 minutes,
- Time = 10 minutes / 60 minutes/hour = 1/6 hour
3. Calculate the speed:
- Speed = Distance / Time
- Speed = 6 km / (1/6 hour) = 6 km × 6 = 36 km/hr
So, the speed of the cyclist is 36 kilometers per hour.
In summary:
- Speed in centimeters per second = 1,000 cm/sec
- Speed in meters per second = 10 m/sec
- Speed in kilometers per hour = 36 km/hr
