An Airplane Traveling 245 M/s 245 \, \text{m/s} 245 M/s East Experiences Turbulence, So The Pilot Slows Down To 230 M/s 230 \, \text{m/s} 230 M/s . It Takes The Pilot 7 Seconds To Slow Down To This Speed. What Is The Acceleration Of The Plane? Round Your Answer

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Understanding the Problem

When an airplane experiences turbulence, the pilot must slow down to maintain control and ensure the safety of the passengers. In this scenario, the airplane is initially traveling at a speed of $245 \, \text{m/s}$ east. The pilot then slows down to a speed of $230 \, \text{m/s}$ over a period of 7 seconds. The problem requires us to find the acceleration of the plane during this time.

Identifying the Given Information

• Initial speed of the airplane: $245 \, \text{m/s}$
• Final speed of the airplane: $230 \, \text{m/s}$
• Time taken to slow down: 7 seconds

Calculating the Acceleration

To find the acceleration of the plane, we can use the following formula:

$$a = \frac{\Delta v}{\Delta t}$$

where $a$ is the acceleration, $\Delta v$ is the change in velocity, and $\Delta t$ is the time taken.

In this case, the change in velocity is the difference between the final speed and the initial speed:

$$\Delta v = v_f - v_i = 230 \, \text{m/s} - 245 \, \text{m/s} = -15 \, \text{m/s}$$

The negative sign indicates that the velocity is decreasing.

The time taken to slow down is given as 7 seconds.

Substituting the Values

Now we can substitute the values into the formula:

$$a = \frac{\Delta v}{\Delta t} = \frac{-15 \, \text{m/s}}{7 \, \text{s}}$$

Calculating the Acceleration

To find the acceleration, we can simplify the expression:

$$a = \frac{-15 \, \text{m/s}}{7 \, \text{s}} = -2.14 \, \text{m/s}^2$$

The negative sign indicates that the acceleration is in the opposite direction to the velocity.

Conclusion

The acceleration of the plane is $-2.14 \, \text{m/s}^2$. This means that the plane is slowing down at a rate of $2.14 \, \text{m/s}^2$.

Importance of Acceleration in Real-World Scenarios

Acceleration plays a crucial role in various real-world scenarios, including:

• Air travel: Understanding acceleration is essential for pilots to navigate through turbulence and ensure the safety of passengers.
• Sports: Athletes must consider acceleration when performing high-speed movements, such as sprinting or jumping.
• Transportation: Acceleration is critical in the design and operation of vehicles, including cars, buses, and trains.

Final Thoughts

In conclusion, the acceleration of the plane can be calculated using the formula $a = \frac{\Delta v}{\Delta t}$. By substituting the given values, we found that the acceleration of the plane is $-2.14 \, \text{m/s}^2$. This demonstrates the importance of understanding acceleration in real-world scenarios, including air travel, sports, and transportation.

Frequently Asked Questions

• What is acceleration? Acceleration is the rate of change of velocity. It is a measure of how quickly an object's velocity changes.
• How is acceleration calculated? Acceleration can be calculated using the formula $a = \frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the time taken.
• What is the unit of acceleration? The unit of acceleration is $\text{m/s}^2$.

References

• Physics for Scientists and Engineers, 3rd edition, by Paul A. Tipler and Gene Mosca
• University Physics, 13th edition, by Hugh D. Young and Roger A. Freedman
  

Understanding Acceleration

Acceleration is a fundamental concept in physics that describes the rate of change of velocity. It is a measure of how quickly an object's velocity changes. In this article, we will answer some of the most frequently asked questions about acceleration.

Q: What is acceleration?

A: Acceleration is the rate of change of velocity. It is a measure of how quickly an object's velocity changes.

Q: How is acceleration calculated?

A: Acceleration can be calculated using the formula $a = \frac{\Delta v}{\Delta t}$, where $\Delta v$ is the change in velocity and $\Delta t$ is the time taken.

Q: What is the unit of acceleration?

A: The unit of acceleration is $\text{m/s}^2$.

Q: What is the difference between velocity and acceleration?

A: Velocity is a measure of an object's speed in a particular direction, while acceleration is a measure of how quickly an object's velocity changes.

Q: Can an object have a constant velocity and still be accelerating?

A: Yes, an object can have a constant velocity and still be accelerating. This occurs when the object is moving in a circular path, such as a car turning a corner.

Q: What is the relationship between force and acceleration?

A: Force and acceleration are related by the equation $F = ma$, where $F$ is the force applied to an object, $m$ is the mass of the object, and $a$ is the acceleration produced.

Q: Can an object have a negative acceleration?

A: Yes, an object can have a negative acceleration. This occurs when the object is slowing down, such as a car braking.

Q: What is the difference between instantaneous acceleration and average acceleration?

A: Instantaneous acceleration is the acceleration of an object at a specific instant in time, while average acceleration is the acceleration of an object over a period of time.

Q: Can an object have a zero acceleration?

A: Yes, an object can have a zero acceleration. This occurs when the object is moving at a constant velocity, such as a car driving on a straight road.

Q: What is the relationship between acceleration and energy?

A: Acceleration is related to energy by the equation $E = \frac{1}{2}mv^2$, where $E$ is the kinetic energy of an object, $m$ is the mass of the object, and $v$ is the velocity of the object.

Q: Can an object have a high acceleration and still be moving at a low speed?

A: Yes, an object can have a high acceleration and still be moving at a low speed. This occurs when the object is accelerating rapidly, such as a car accelerating from a standstill.

Q: What is the difference between linear acceleration and angular acceleration?

A: Linear acceleration is the acceleration of an object in a straight line, while angular acceleration is the acceleration of an object in a circular path.

Q: Can an object have a high angular acceleration and still be moving at a low speed?

A: Yes, an object can have a high angular acceleration and still be moving at a low speed. This occurs when the object is rotating rapidly, such as a car turning a corner.

Q: What is the relationship between acceleration and time?

A: Acceleration is related to time by the equation $a = \frac{\Delta v}{\Delta t}$, where $a$ is the acceleration, $\Delta v$ is the change in velocity, and $\Delta t$ is the time taken.

Q: Can an object have a high acceleration and still be moving at a constant speed?

A: Yes, an object can have a high acceleration and still be moving at a constant speed. This occurs when the object is accelerating in a circular path, such as a car driving on a circular track.

Q: What is the difference between acceleration and jerk?

A: Acceleration is the rate of change of velocity, while jerk is the rate of change of acceleration.

Q: Can an object have a high jerk and still be moving at a low speed?

A: Yes, an object can have a high jerk and still be moving at a low speed. This occurs when the object is accelerating rapidly, such as a car accelerating from a standstill.

Q: What is the relationship between acceleration and the force of friction?

A: Acceleration is related to the force of friction by the equation $F_f = \mu N$, where $F_f$ is the force of friction, $\mu$ is the coefficient of friction, and $N$ is the normal force.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of friction?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of friction. This occurs when the object is sliding on a rough surface, such as a car sliding on a wet road.

Q: What is the difference between acceleration and deceleration?

A: Acceleration is the rate of change of velocity, while deceleration is the rate of change of velocity in the opposite direction.

Q: Can an object have a high deceleration and still be moving at a low speed?

A: Yes, an object can have a high deceleration and still be moving at a low speed. This occurs when the object is slowing down rapidly, such as a car braking.

Q: What is the relationship between acceleration and the force of gravity?

A: Acceleration is related to the force of gravity by the equation $a = g$, where $a$ is the acceleration due to gravity and $g$ is the acceleration due to gravity.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of gravity?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of gravity. This occurs when the object is falling under the influence of gravity, such as a ball falling from a height.

Q: What is the difference between acceleration and velocity?

A: Acceleration is the rate of change of velocity, while velocity is a measure of an object's speed in a particular direction.

Q: Can an object have a high velocity and still be accelerating?

A: Yes, an object can have a high velocity and still be accelerating. This occurs when the object is moving in a circular path, such as a car turning a corner.

Q: What is the relationship between acceleration and the force of a spring?

A: Acceleration is related to the force of a spring by the equation $F = kx$, where $F$ is the force of the spring, $k$ is the spring constant, and $x$ is the displacement of the spring.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of a spring?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of a spring. This occurs when the object is oscillating on a spring, such as a mass-spring system.

Q: What is the difference between acceleration and the force of a damper?

A: Acceleration is the rate of change of velocity, while the force of a damper is the force that opposes the motion of an object.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of a damper?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of a damper. This occurs when the object is moving through a fluid, such as a car moving through water.

Q: What is the relationship between acceleration and the force of a motor?

A: Acceleration is related to the force of a motor by the equation $F = ma$, where $F$ is the force of the motor, $m$ is the mass of the object, and $a$ is the acceleration produced.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of a motor?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of a motor. This occurs when the object is being accelerated by a motor, such as a car accelerating from a standstill.

Q: What is the difference between acceleration and the force of a brake?

A: Acceleration is the rate of change of velocity, while the force of a brake is the force that opposes the motion of an object.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of a brake?

A: Yes, an object can have a high acceleration and still be moving at a low speed due to the force of a brake. This occurs when the object is braking, such as a car braking on a wet road.

Q: What is the relationship between acceleration and the force of a propeller?

A: Acceleration is related to the force of a propeller by the equation $F = ma$, where $F$ is the force of the propeller, $m$ is the mass of the object, and $a$ is the acceleration produced.

Q: Can an object have a high acceleration and still be moving at a low speed due to the force of a propeller?

A: Yes, an object can have a high acceleration and still be moving