What is the average speed of a cheetah that runs 88 m in 5 seconds?
a) In m/s
b) In miles/hour (recall conversion factors 1 m = 3.3 feet, 5280 ft = 1 mi, 3600 s = 1 hour)
The correct answer and explanation is :
Let’s solve it carefully:
First: Find the average speed in meters per second (m/s).
Speed = Distance ÷ Time
Given:
- Distance = 88 meters
- Time = 5 seconds
[
\text{Speed} = \frac{88 \, \text{m}}{5 \, \text{s}} = 17.6 \, \text{m/s}
]
✅ So the answer for (a) is 17.6 m/s.
Second: Convert that speed into miles per hour (mi/hr).
We’ll go step-by-step through the unit conversions:
- Meters to feet:
Since 1 meter = 3.3 feet:
[
88 \, \text{m} \times 3.3 = 290.4 \, \text{feet}
]
- Feet per second:
Now, in 5 seconds:
[
\text{Feet per second} = \frac{290.4 \, \text{feet}}{5 \, \text{seconds}} = 58.08 \, \text{ft/s}
]
- Feet per hour:
Multiply by the number of seconds in an hour (3600):
[
58.08 \times 3600 = 209088 \, \text{feet/hour}
]
- Feet to miles:
Since 5280 feet = 1 mile:
[
\text{Miles/hour} = \frac{209088}{5280} \approx 39.6 \, \text{mi/hr}
]
✅ So the answer for (b) is approximately 39.6 miles per hour.
Final Answers:
- (a) 17.6 m/s
- (b) 39.6 miles/hour
📚 Full Explanation (around 300+ words):
To find the average speed of an object, you divide the total distance traveled by the time it took. In this case, the cheetah ran 88 meters in 5 seconds. Dividing 88 by 5 gives 17.6 meters per second (m/s). This tells us that for every second that passed, the cheetah covered 17.6 meters.
Often, it’s important to express speeds in different units depending on the situation. In daily life, especially in the U.S., speed is often measured in miles per hour (mph or mi/hr). So, we need to convert meters per second to miles per hour.
First, we convert meters to feet because it’s easier to connect to miles. Since 1 meter equals 3.3 feet, we multiply 88 meters by 3.3 to get 290.4 feet. Then, we calculate how many feet the cheetah runs per second, which is 290.4 divided by 5, giving 58.08 feet per second.
Next, to find out how many feet the cheetah runs in an hour, we multiply by the number of seconds in an hour (3600 seconds). This results in 209,088 feet per hour. Since 1 mile equals 5,280 feet, we divide 209,088 by 5,280 to convert feet into miles, arriving at approximately 39.6 miles per hour.
This process shows how important unit conversions are when solving real-world physics problems. A cheetah is known as the fastest land animal, and reaching around 40 miles per hour in just 5 seconds shows its remarkable acceleration and speed. In fact, cheetahs can reach even higher speeds over short bursts when hunting, often exceeding 60 miles per hour!