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

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

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

Answer :

To find the mass of the crate, we can use Newton's second law of motion, which is expressed by the formula [tex]\( F = ma \)[/tex]. Here, [tex]\( F \)[/tex] represents the force in newtons (N), [tex]\( m \)[/tex] is the mass in kilograms (kg), and [tex]\( a \)[/tex] is the acceleration in meters per second squared ([tex]\( m/s^2 \)[/tex]).

### Step-by-step solution:

1. Identify the given values:
- The force [tex]\( F \)[/tex] is 200 N.
- The acceleration [tex]\( a \)[/tex] is [tex]\( 8 \, m/s^2 \)[/tex].

2. Rearrange the formula to solve for the mass [tex]\( m \)[/tex]:
[tex]\[
m = \frac{F}{a}
\][/tex]

3. Substitute the known values into the equation:
[tex]\[
m = \frac{200 \, \text{N}}{8 \, m/s^2}
\][/tex]

4. Calculate the mass:
[tex]\[
m = 25 \, \text{kg}
\][/tex]

Therefore, the mass of the crate is 25 kg.

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