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Answer :
To find the acceleration of the 22 kg object, we need to use Newton's Second Law of Motion, which states that the net force acting on an object is equal to the product of its mass and acceleration. The formula is:
[tex]\[ F_{\text{net}} = m \cdot a \][/tex]
where:
- [tex]\( F_{\text{net}} \)[/tex] is the net force acting on the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
Step-by-step, here's how we can solve this problem:
1. Identify the Forces:
- The forward force acting on the object is 90 N.
- The backward force acting on the object is 145 N.
2. Calculate the Net Force:
- Since the forces are in opposite directions, we find the net force by subtracting the backward force from the forward force:
[tex]\[
F_{\text{net}} = 90 \, \text{N} - 145 \, \text{N} = -55 \, \text{N}
\][/tex]
3. Note on the Net Force:
- The net force is negative because the backward force is greater than the forward force, indicating the object is experiencing a net force in the backward direction.
4. Calculate the Acceleration:
- We use the formula for Newton's second law rearranged to solve for acceleration:
[tex]\[
a = \frac{F_{\text{net}}}{m}
\][/tex]
- Substitute the known values:
[tex]\[
a = \frac{-55 \, \text{N}}{22 \, \text{kg}} = -2.5 \, \text{m/s}^2
\][/tex]
5. Interpret the Acceleration:
- The negative acceleration indicates that the object is accelerating in the opposite direction to the forward force.
Thus, the acceleration of the object is [tex]\(-2.5 \, \text{m/s}^2\)[/tex].
[tex]\[ F_{\text{net}} = m \cdot a \][/tex]
where:
- [tex]\( F_{\text{net}} \)[/tex] is the net force acting on the object,
- [tex]\( m \)[/tex] is the mass of the object,
- [tex]\( a \)[/tex] is the acceleration of the object.
Step-by-step, here's how we can solve this problem:
1. Identify the Forces:
- The forward force acting on the object is 90 N.
- The backward force acting on the object is 145 N.
2. Calculate the Net Force:
- Since the forces are in opposite directions, we find the net force by subtracting the backward force from the forward force:
[tex]\[
F_{\text{net}} = 90 \, \text{N} - 145 \, \text{N} = -55 \, \text{N}
\][/tex]
3. Note on the Net Force:
- The net force is negative because the backward force is greater than the forward force, indicating the object is experiencing a net force in the backward direction.
4. Calculate the Acceleration:
- We use the formula for Newton's second law rearranged to solve for acceleration:
[tex]\[
a = \frac{F_{\text{net}}}{m}
\][/tex]
- Substitute the known values:
[tex]\[
a = \frac{-55 \, \text{N}}{22 \, \text{kg}} = -2.5 \, \text{m/s}^2
\][/tex]
5. Interpret the Acceleration:
- The negative acceleration indicates that the object is accelerating in the opposite direction to the forward force.
Thus, the acceleration of the object is [tex]\(-2.5 \, \text{m/s}^2\)[/tex].
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