To find the acceleration of Deep Space 1, you can use Newton's second law of motion, which states that \( F = m \cdot a \), where \( F \) is the net force, \( m \) is the mass, and \( a \) is the acceleration.
Rearranging this equation to solve for acceleration \( a \) gives you:
\[ a = \frac{F}{m} \]
In this case, the net force \( F \) is \( 0.10 , N \) and the mass \( m \) is \( 500 , kg \). So, the expression you would use to find the spacecraft's acceleration is:
\[ a = \frac{0.10 , N}{500 , kg} \]
None of the provided options A, B, C, or D are complete expressions that directly show this calculation, but the appropriate choice based on this context would be the one that represents \( F = m \cdot a \), which is closest to:
Option A (if it shows the correct relationship).
To summarize, the acceleration \( a \) can be expressed as \( a = \frac{0.10 , N}{500 , kg} \). If none of the options explicitly show that, the question might be about identifying a relevant relationship rather than calculating a specific value.