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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