Find the  x- and  y-components of the vector  v⃗  = (5.0  cm/s ,  −x-direction).

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.

Find the x- and y-components of the vector v⃗ = (5.0 cm/s , −x-direction).

Learn how to find the x- and y-components of a vector with a magnitude of 5.0 cm/s in the negative x-direction. This problem covers vector decomposition, essential for understanding physics and math concepts related to motion in 1D and coordinate systems. Suitable for students in Grades 9-12.

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