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Find the x-component of [tex]\vec{a} = (7.5 \, \text{m/s}^2, \text{negative x-direction})[/tex].

A. 7.5 m/s\(^2\)
B. -7.5 m/s\(^2\)
C. 7.5 m/s
D. -7.5 m/s

Answer :

Final answer:

The x-component of a vector a⃗ = (7.5 m/s^2 , negative x-direction) is -7.5 m/s^2. In Physics, the sign of a vector's components accounts for its direction.

Explanation:

In this question, we're asked to find the x-component of a vector a⃗ that points in the negative x-direction. The vector a⃗ given here already has the magnitude (7.5 m/s^2). However, because it is specified to be in the negative x-direction, we must take the negative of this magnitude. Therefore, the x-component of the vector a⃗ is -7.5 m/s^2.

This falls under the concept of vectors in Physics, where direction influences the sign of the vector's components. In a coordinate system, a positive component usually refers to the x-direction to the right or the y-direction upwards — which are arbitrary standards — while a negative component represents the opposite directions.

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