To find the acceleration of an object given the force applied and the mass of the object, we'll use Newton's second law of motion, which is expressed by the formula:
[tex]\[ F = ma \][/tex]
where:
- [tex]\( F \)[/tex] is the force applied (in Newtons),
- [tex]\( m \)[/tex] is the mass of the object (in kilograms),
- [tex]\( a \)[/tex] is the acceleration (in meters per second squared, [tex]\( \text{m/s}^2 \)[/tex]).
Given:
- The force [tex]\( F = 5 \)[/tex] Newtons.
- The mass [tex]\( m = 50 \)[/tex] grams.
The first step is to convert the mass from grams to kilograms because the standard unit of mass in the formula is kilograms.
1. Convert mass to kilograms:
[tex]\[ 1 \text{ kilogram (kg)} = 1000 \text{ grams (g)} \][/tex]
Thus,
[tex]\[ m = \frac{50 \text{ g}}{1000 \text{ g/kg}} = 0.05 \text{ kg} \][/tex]
2. Rearrange the formula to solve for acceleration [tex]\( a \)[/tex]:
[tex]\[ a = \frac{F}{m} \][/tex]
3. Calculate the acceleration:
Substitute the given values into the formula:
[tex]\[ a = \frac{5 \text{ N}}{0.05 \text{ kg}} = 100 \text{ m/s}^2 \][/tex]
Therefore, the acceleration of the object is [tex]\( 100 \)[/tex] m/s².
Among the given options, the correct answer is:
[tex]\[ 100 \text{ m/s}^2 \][/tex]
