91Ó°ÊÓ

Acceleration is a key concept in kinematics, which is the study of motion. It describes how quickly the velocity of an object changes over time. Imagine pressing the accelerator in a car; the harder you press, the quicker the car speeds up. Similarly, acceleration in physics tells us how fast an object's speed or velocity is changing.
In our exercise, the electrons experience an acceleration of \(5 \times 10^{14} \, \text{m/s}^2\). This means their velocity increases by this amount every second during the acceleration phase. This incredibly high rate is achievable due to the electrons' tiny mass, allowing them to reach high velocities quickly.

• Initial Velocity \( u \): Prior to acceleration, the velocity of the electrons is zero, as they start from rest.
• Acceleration \( a \): Provided as \(5 \times 10^{14} \, \text{m/s}^2\) in the problem.

Understanding these parameters helps us predict how the electrons will behave under force.

Final Velocity represents the speed an object achieves after a period of acceleration. It's like when a car reaches a certain speed after accelerating from a stop.
To calculate this for the electrons, we use one of the kinematic equations: \[ v^2 = u^2 + 2as \] Here, \( v \) is the final velocity, \( u \) is the initial velocity (\(0\) in our scenario), \( a \) is acceleration, and \( s \) is the distance traveled. Plugging in the values, \[ v^2 = 0 + 2(5 \times 10^{14})(0.15) \] Solving gives us \( v^2 = 1.5 \times 10^{14} \). Taking the square root, we find \[ v = \sqrt{1.5 \times 10^{14}} \approx 1.225 \times 10^7 \, \text{m/s} \] This impressive velocity indicates how swiftly the electrons are moving after acceleration.

Kinematic equations are powerful tools in physics to solve problems involving motion. They link several motion variables: initial velocity, final velocity, acceleration, time, and displacement.

• One such equation used in our problem is \( v^2 = u^2 + 2as \).
• Another equation employed is \( v = u + at \), where \( t \) is the time of acceleration.

These equations allow you to solve for unknown variables when you have sufficient known values. For example, in our exercise, we used them to find how fast the electrons moved and how long it took. By understanding these relationships, you can predict various aspects of motion easily. It's like having a recipe that tells you what ingredients you need and how long to cook.