Problem 36 - Algebra 1

Question

In 5 seconds, an athlete runs 40 feet.

Step-by-Step Solution

Answer

The athlete's velocity is 8 feet per second.

Step 1: Understand the Given Information

You are given that an athlete runs 40 feet in 5 seconds. This information can be used to calculate the athlete's velocity using the formula: velocity = distance/time.

Step 2: Substitute the Values into the Formula

You should replace 'distance' with 40 feet and 'time' with 5 seconds in the velocity formula. So, it becomes: velocity = 40 feet / 5 seconds.

Step 3: Solve for Velocity

After substituting the values into the formula, you should divide 40 feet by 5 seconds to find the velocity. By doing this, you will find that the velocity is 8 feet per second.

Key Concepts

Distance and Time

When we talk about velocity, understanding the relationship between distance and time is essential. Distance refers to how much ground an object covers while moving from one point to another. It is measured in units such as feet, meters, or miles.
Time, on the other hand, is how long it takes for the object to move from one point to the other, typically measured in seconds, minutes, or hours.
Consider an athlete who runs a specific distance in a measured amount of time. If this athlete runs 40 feet in 5 seconds, both distance (40 feet) and time (5 seconds) are crucial pieces of information. These quantities allow us to calculate how fast the athlete is running, which brings us to the concept of velocity.
The formula that relates these three elements is:

• Velocity = Distance / Time

This simple relationship helps us understand how quickly an object or person travels a certain distance within a given time frame.

Units of Measurement

When computing velocity, units of measurement play a crucial role. They give meaning to the numerical results and help in making comparisons across different scenarios.
In the context of the exercise, the distance was given in feet and the time in seconds. Therefore, the velocity was expressed in feet per second (ft/s). This unit tells us how many feet the athlete runs in each second.
Having consistent units ensures accuracy in calculations. If the distance were given in meters and the time in seconds, the velocity would become meters per second (m/s).
To convert units, you need a conversion factor. For example, to convert feet to meters, use the factor 1 foot ≈ 0.3048 meters.
Proper use of units not only aids in precise calculations but also helps to effectively communicate information. For example, a velocity of 8 feet per second is straightforward to interpret because it clearly states how fast the athlete is moving in each second.

Rate of Speed

Rate of speed, also known as velocity when direction is not a consideration, describes how fast something is moving. In simple terms, it is the distance covered in a specific unit of time.
Using the formula for velocity, we calculated the athlete's rate of speed as 8 feet per second. This means that for every second the athlete runs, they cover a distance of 8 feet.
Understanding rate of speed is crucial in everyday life:

• Travel Planning: It helps determine how long it will take to reach a destination if you know the speed.
• Exercise Monitoring: Knowing your speed can help in pacing workouts and improving performance.

Interpreting rate of speed involves both numbers and units. This makes it a fundamental aspect of subjects like physics, where it is essential to calculate and understand motion.
The concept becomes more complex when direction is involved, leading us to the concept of vector velocity. However, for simple cases like this exercise, understanding rate of speed or velocity without direction is sufficient.