91Ó°ÊÓ

Kinetic energy is the energy an object possesses due to its motion. When it comes to the kinetic energy formula, it is very straightforward.
The formula is given by: \[ KE = \frac{1}{2}mv^2 \]
Let's break this down:

• \( KE \) is the kinetic energy.
  It is typically measured in Joules (J).
  
• \( m \) is the mass of the object.
  Mass is usually measured in kilograms (kg).
  
• \( v \) is the velocity of the object.
  Velocity is measured in meters per second (m/s).
  

In simple terms, the kinetic energy of an object increases with its mass and velocity. When you look at the formula, the velocity is squared (\( v^2 \)), meaning that the kinetic energy increases with the square of the object's speed.

Whenever you need to find the kinetic energy of an object, just substitute the mass and the velocity into the formula and solve it to find the kinetic energy.
This fundamental formula will be very useful in solving many problems related to motion and energy.

Understanding the mass of an electron is crucial when dealing with calculations in quantum mechanics and other fields in physics.
The mass of an electron is very tiny compared to everyday objects.
Its precise value is \( 9.11 \times 10^{-31} \) kilograms (kg).
To put this into perspective, this makes the electron about 1836 times lighter than a proton.
Despite its small mass, the electron plays a significant role in many physical phenomena, such as electricity and magnetism.

In our specific problem, knowing the mass of an electron allows us to calculate its speed when given its kinetic energy. Because of its tiny mass, electrons can achieve very high speeds even with relatively small amounts of energy.

Calculating the velocity of an electron involves rearranging the kinetic energy formula to solve for velocity.
Starting from the kinetic energy formula: \( KE = \frac{1}{2}mv^2 \)
We want to solve for \( v \), the velocity.

Here’s how we can do that step-by-step:

• Multiply both sides by 2: \[ 2 \times KE = mv^2 \]
• Divide both sides by \( m \): \[ v^2 = \frac{2 \times KE}{m} \]
• Take the square root of both sides to solve for \( v \): \[ v = \sqrt{\frac{2 \times KE}{m}} \]

Now, let’s plug in the values given in the original exercise:
Kinetic energy \( KE = 6.7 \times 10^{-19} \text{ J} \)
Mass of the electron \( m = 9.11 \times 10^{-31} \text{ kg} \)

Substituting these values into our formula:
\[ v = \sqrt{ \frac{ 2 \times 6.7 \times 10^{-19} }{ 9.11 \times 10^{-31} }} \]

First, calculate the expression inside the square root:
\[ \frac{2 \times 6.7 \times 10^{-19}}{ 9.11 \times 10^{-31}} = 1.47 \times 10^{12} \]

Next, take the square root of the result:
\[ v = \sqrt{1.47 \times 10^{12}} \approx 1.21 \times 10^6 \; \text{m/s} \]

Therefore, the speed of the electron is approximately \( 1.21 \times 10^6 \) meters per second. This method can be used to find the velocity of any object when its mass and kinetic energy are known.