91Ó°ÊÓ

In kinematics, uniform acceleration means an object's acceleration remains constant over time. It's a key idea when analyzing motion under the influence of constant forces, such as gravity or in this case, the electric force acting between charged plates.

Uniform acceleration is particularly useful for understanding how an object's velocity and position change. When we deal with uniform acceleration, we often use the kinematic equations:

• To find the displacement: \( s = v_0 t + \frac{1}{2} a t^2 \)
• To find the final velocity: \( v = v_0 + a t \)

Here, \( v_0 \) is the initial velocity, \( a \) is the acceleration, \( t \) is the time, and \( s \) is the displacement.

In the given problem, the electron experiences a constant downward acceleration of \(1.00 \times 10^{17} \text{ cm/s}^2\), which allows us to apply these equations to determine how far it travels vertically and how its velocity changes over time.

Objects that move along a path affected by forces can have both horizontal and vertical components of motion. Understanding these two components separately helps in solving complex motion problems.

Horizontal motion often involves constant velocity, meaning no horizontal force is acting on the object. This can be derived from the formula: \[\text{Velocity} = \frac{\text{Distance}}{\text{Time}}.\]

Vertical motion usually includes acceleration due to forces like gravity or electric fields. We calculate this using kinematic equations for uniformly accelerated motion.

In the exercise, the electron maintains a constant horizontal velocity (\(1.00 \times 10^9\text{ cm/s}\)) while facing downward acceleration from the charged plates, which affect its vertical movement. By calculating separately, we can find how far it goes horizontally without any change in speed and how much its path curves due to vertical forces.

Velocity components are essential for breaking down an object's overall movement into manageable parts. We usually split velocity into horizontal and vertical components, especially when analyzing projectiles or objects in motion under multiple forces.

In this exercise, the electron starts with a significant horizontal velocity (\(1.00 \times 10^9\text{ cm/s}\)) and no initial vertical velocity. The lack of horizontal acceleration means the horizontal velocity remains constant.

Vertical velocity, however, changes due to uniform acceleration. By the formula \( v = v_0 + a t \), where the initial vertical velocity \( v_0 \) is zero, we calculate the vertical velocity component by multiplying acceleration by time (\(2.00 \times 10^{-9}\text{ s}\) in this case). The result yields the final vertical velocity of \(2.00 \times 10^8\text{ cm/s}\), showing how differently each component behaves under various forces.