Problem 53 - Algebra 1: Concepts and Skills

Question

Find the velocity of the object. A submarine descends 21 meters in 2 seconds.

Step-by-Step Solution

Answer

The velocity of the submarine is -10.5 m/s in the downward direction.

Step 1: Identifying the Given Values

In this scenario, a submarine descends by 21 meters in 2 seconds. These given values represent the displacement (21 meters) and the time interval (2 seconds) respectively

Step 2: Applying the Velocity Formula

Velocity is defined as displacement divided by the time interval. In this case, the displacement is -21 meters (since the submarine is descending, we take the value as negative) and the time is 2 seconds. So, we can represent this as \(v = \frac{-21}{2}\)

Step 3: Calculating the Velocity

By performing the operation in the equation we get \(v = -10.5 \, m/s\). The negative value indicates the direction of the motion, which is downward in this case

Key Concepts

Understanding Displacement

Displacement is a fundamental concept in the study of motion and is a vector quantity. This means it has both magnitude and direction. Displacement refers to the change in position of an object.
It is different from distance, which only measures the magnitude without direction. In the case of the submarine, the displacement is the 21 meters it descends. Since direction matters for displacement, when dealing with downward or vertical motion, we often indicate this with a negative sign.
So for our submarine example, the displacement is represented as

• -21 meters because the motion is downward.

It’s essential to always note the direction when calculating velocity or any other vector-related measurements.

Defining Time Interval

The time interval is another critical element in understanding motion. It is simply the duration over which the motion occurs. This is often measured in seconds, minutes, or hours, depending on the context.
For the submarine example, the time interval given is 2 seconds. This tells us how long it took for the submarine to descend 21 meters. Knowing the time interval allows us to compute other motion-related quantities such as velocity. When combined with displacement in calculations, the time interval helps us gain insights into how fast something is moving.
In most physics problems, keeping track of the correct time interval is crucial for accurate results.

Exploring Descent

Descent is a term used to describe downward motion. In many contexts, like aviation and submarine travel, descent is a common term used to signify moving toward the Earth. Thus, it's associated with a negative displacement when dealing with motion vectors.
When the submarine descends, it means it travels vertically downward through the water. This can involve adjustments in buoyancy and propulsion to control the rate of descent. By understanding descent, we account for the direction in motion calculations, particularly in determining velocity.Velocity during a descent is important because it not only tells us how fast the object is moving, but also in which direction. Negative velocity, as calculated for the submarine, confirms the downward direction:

• Negative value in \( v = -10.5 \, m/s \) indicates descent.

Understanding descent is crucial in physics for predicting and analyzing the behavior of objects moving up and down.