91Ó°ÊÓ

Unit conversion is an essential skill in physics and engineering, particularly when dealing with different measurement systems. Often, you'll encounter values in units that need to be consistent to make calculations easier.
Let's focus on converting speed from miles per hour (mi/h) to meters per second (m/s), which is critical when working with distances in meters and time in seconds.
To do this conversion, you use specific conversion factors:

• 1 mile = 1609.34 meters
• 1 hour = 3600 seconds

In our exercise, the jet's speed is given as 155 mi/h. To convert this to m/s:Step 1: Multiply the speed by the number of meters in a mile:\[155 ext{ mi/h} \times \frac{1609.34 ext{ m}}{1 ext{ mi}}\]Step 2: Divide by the number of seconds in an hour:\[\frac{249418.7 ext{ m}}{3600 ext{ s}}\]This calculation simplifies to approximately 69.3 m/s. Hence, converting units properly ensures you can plug values directly into formulas without errors.

Acceleration is the rate of change of velocity of an object. It is a vector quantity, meaning it has both magnitude and direction.
In physics problems, acceleration tells us how fast an object is speeding up or slowing down.
To calculate acceleration when the initial velocity (\(v_i\)) and final velocity (\(v_f\)) are known, you can use:

• \(a = \frac{\Delta v}{\Delta t}\)

Where \(\Delta v\) is the change in velocity and \(\Delta t\) is the change in time.In our scenario, the jet accelerates from 0 m/s to 69.3 m/s over 2 seconds:

• Change in velocity (\(\Delta v\)): 69.3 m/s
• Time interval (\(\Delta t\)): 2 seconds
• Acceleration (\(a\)): \(\frac{69.3 \text{ m/s}}{2\text{ s}} = 34.65 \text{ m/s}^2\)

Understanding acceleration helps us comprehend how forces affect motion, such as the immediate speed-up of a jet leaving an aircraft carrier.

Determining mass in physics often involves understanding and applying Newton's laws of motion. Newton's Second Law states that Force = mass × acceleration, or \(F = m \cdot a\). This relationship is pivotal in calculating mass when force and acceleration are given.
In the example of the jet on an aircraft carrier, the force exerted by the catapult is known (\(F = 9.35 \times 10^5 \text{ N}\)), and we've calculated the acceleration (\(a = 34.65 \text{ m/s}^2\)). We aim to find the mass (\(m\)): To solve for mass, rearrange Newton's Second Law:

• \(m = \frac{F}{a}\)

Plug in the values:\[m = \frac{9.35 \times 10^5}{34.65} \approx 26983 \text{ kg}\]This calculation shows that by knowing only the force and acceleration, you can find the mass, demonstrating the profound interconnection between these physical quantities.