The vector $\vec{v} = (5.0 \, \text{cm/s}, -x\text{-direction})$ is a one-dimensional vector pointing entirely along the negative x-axis. Here's how you can find the x- and y-components:

Given:

• Magnitude of the velocity: $5.0 \, \text{cm/s}$
• Direction: $-x\text{-direction}$

x-Component:

Since the vector is entirely along the x-axis, the x-component is equal to the magnitude of the vector but negative because it points in the negative x-direction. $v_x = -5.0 \, \text{cm/s}$

y-Component:

There is no component along the y-axis, so the y-component is zero. $v_y = 0 \, \text{cm/s}$

Final Result:

• $v_x = -5.0 \, \text{cm/s}$
• $v_y = 0 \, \text{cm/s}$

Would you like more details or have any questions?

Here are some related questions:

1. What are the components of a vector in the positive y-direction?
2. How do you calculate the magnitude of a vector from its components?
3. What happens if a vector has a negative y-component?
4. How do you represent a vector in terms of unit vectors $\hat{i}$ and $\hat{j}$?
5. How would you find the components of a vector if it pointed at an angle?

Tip: Always be mindful of the direction of a vector when calculating its components, especially when they involve negative values.