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------------------------------------------------ What is the mass of a crate if a force of 200 N causes it to accelerate at [tex]$8 \, \text{m/s}^2$[/tex]?

(Formula: [tex][tex]$F = ma$[/tex][/tex])

A. 25 kg
B. 192 kg
C. 208 kg
D. 16 kg

By Newton's Second Law of Motion, if the mass ([tex]m[/tex]) of an object stays constant, acceleration ([tex]a[/tex]) of the object would be proportional to the net force ([tex]F_{\text{net}}[/tex]) on the object:

[tex]\displaystyle a = \frac{F_{\text{net}}}{m}[/tex].

In this question, it is given that:

Net force on the object is [tex]F_{\text{net}} = 200\; {\rm N}[/tex], and
Acceleration of the object is [tex]a = 8\; {\rm m\cdot s^{-1}[/tex].

To find the mass ([tex]m[/tex]) of the object under these assumptions, rearrange the equation and solve for mass:

[tex]\displaystyle m = \frac{F_{\text{net}}}{a} = \frac{200\; {\rm N}}{8\; {\rm m\cdot s^{-2}}} = 25\; {\rm kg}[/tex].

(Note that [tex]1\; {\rm N} = 1\; {\rm kg\cdot m\cdot s^{-2}}[/tex].)

In other words, the mass of this object would be [tex]25\; {\rm kg}[/tex] to ensure that acceleration would be [tex]8\; {\rm m\cdot s^{-2}}[/tex] when net force on the object is [tex]200\; {\rm N}[/tex].