Question

A moving electron accelerates at 5200 m/s² in a 55.0 degree direction. After 0.530 s, it has a velocity of 6598 m/s in a -20.5 degree direction. What is the x-component of the initial velocity?

Answer 1

The x-component of the initial velocity of an electron can be calculated by breaking down the final velocity into x and y components, finding the acceleration components, and using the kinematic equation.

Step-by-step explanation:

To find the x-component of the initial velocity of an electron that accelerates at 5200 m/s² in a 55.0 degree direction and has a final velocity of 6598 m/s in a -20.5 degree direction after 0.530 s, we first need to find the change in velocity.

The final velocity can be broken down into x and y components using trigonometry:

• Vfx = 6598 m/s × cos(-20.5 degrees)
• Vfy = 6598 m/s × sin(-20.5 degrees)

Similarly, we can find the acceleration components:

• Ax = 5200 m/s² × cos(55.0 degrees)
• Ay = 5200 m/s² × sin(55.0 degrees)

Using the kinematic equation Vf = Vi + at for the x-component, we identify the initial x-component (Vix) of velocity:

• Vix = Vfx - Ax × t

Substituting the values:

• Vix = (6598 m/s × cos(-20.5 degrees)) - (5200 m/s² × cos(55.0 degrees) × 0.530 s)

The student can now perform the calculations to find the x-component of the initial velocity.