Answer :
To determine the mass of a crate given that a force of 200 N causes it to accelerate at [tex]\(8 \, \text{m/s}^2\)[/tex], you can use the formula for force, which is:
[tex]\[ F = ma \][/tex]
Where:
- [tex]\( F \)[/tex] is the force in Newtons (N)
- [tex]\( m \)[/tex] is the mass in kilograms (kg)
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s[tex]\(^2\)[/tex])
We need to solve for [tex]\( m \)[/tex] (mass). Rearrange the formula to isolate [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, \text{m/s}^2} \][/tex]
[tex]\[ m = 25 \, \text{kg} \][/tex]
So, the mass of the crate is:
[tex]\[ 25 \, \text{kg} \][/tex]
Therefore, the correct answer is:
[tex]\[ 25 \, \text{kg} \][/tex]
[tex]\[ F = ma \][/tex]
Where:
- [tex]\( F \)[/tex] is the force in Newtons (N)
- [tex]\( m \)[/tex] is the mass in kilograms (kg)
- [tex]\( a \)[/tex] is the acceleration in meters per second squared (m/s[tex]\(^2\)[/tex])
We need to solve for [tex]\( m \)[/tex] (mass). Rearrange the formula to isolate [tex]\( m \)[/tex]:
[tex]\[ m = \frac{F}{a} \][/tex]
Now, substitute the given values into the equation:
[tex]\[ m = \frac{200 \, \text{N}}{8 \, \text{m/s}^2} \][/tex]
[tex]\[ m = 25 \, \text{kg} \][/tex]
So, the mass of the crate is:
[tex]\[ 25 \, \text{kg} \][/tex]
Therefore, the correct answer is:
[tex]\[ 25 \, \text{kg} \][/tex]
