Question
A newon force actos on a 3 kg mass for 6 seconds the change of velocity of the mass is
reference sheet:
= ma
a = v/t
reference sheet:
= ma
a = v/t
Answers
GPT-4o mini
To determine the change in velocity of a mass when a force acts on it, we can use Newton's second law of motion, which states:
\[
F = ma
\]
where \( F \) is the force, \( m \) is the mass (in kg), and \( a \) is the acceleration (in m/s²).
From the equation \( a = \frac{v}{t} \), we can also express acceleration in terms of change in velocity (\( \Delta v \)) over time (\( t \)):
\[
a = \frac{\Delta v}{t}
\]
### Steps to find the change in velocity:
1. ** Calculate the acceleration**:
Rearranging the equation for force gives us:
\[
a = \frac{F}{m}
\]
2. **Relate acceleration to change in velocity**:
Since acceleration can also be expressed as the change in velocity over time:
\[
a = \frac{\Delta v}{t}
\]
3. **Solve for \(\Delta v\)**:
This gives us:
\[
\Delta v = a \cdot t
\]
### Application:
Assuming we know the force acting on the mass, we can calculate \( \Delta v \) as follows:
- Let’s say \( F \) is the force (in newtons).
- The mass \( m \) is \( 3 \) kg and time \( t \) is \( 6 \) seconds.
Substituting the values into our equations, we can find the change in velocity once we have the force.
### Example:
If we assume a force of, for example, 12 N is acting on the 3 kg mass:
1. Calculate the acceleration:
\[
a = \frac{F}{m} = \frac{12 \, \text{N}}{3 \, \text{kg}} = 4 \, \text{m/s}^2
\]
2. Calculate the change in velocity:
\[
\Delta v = a \cdot t = 4 \, \text{m/s}^2 \cdot 6 \, \text{s} = 24 \, \text{m/s}
\]
Therefore, the change in velocity of the mass would be \( 24 \, \text{m/s} \) given a force of \( 12 \, \text{N} \).
### Conclusion:
To fully determine the change in velocity, you will need the specific value of the force acting on the mass. You can then substitute that into the equations to find \( \Delta v \).
\[
F = ma
\]
where \( F \) is the force, \( m \) is the mass (in kg), and \( a \) is the acceleration (in m/s²).
From the equation \( a = \frac{v}{t} \), we can also express acceleration in terms of change in velocity (\( \Delta v \)) over time (\( t \)):
\[
a = \frac{\Delta v}{t}
\]
### Steps to find the change in velocity:
1. ** Calculate the acceleration**:
Rearranging the equation for force gives us:
\[
a = \frac{F}{m}
\]
2. **Relate acceleration to change in velocity**:
Since acceleration can also be expressed as the change in velocity over time:
\[
a = \frac{\Delta v}{t}
\]
3. **Solve for \(\Delta v\)**:
This gives us:
\[
\Delta v = a \cdot t
\]
### Application:
Assuming we know the force acting on the mass, we can calculate \( \Delta v \) as follows:
- Let’s say \( F \) is the force (in newtons).
- The mass \( m \) is \( 3 \) kg and time \( t \) is \( 6 \) seconds.
Substituting the values into our equations, we can find the change in velocity once we have the force.
### Example:
If we assume a force of, for example, 12 N is acting on the 3 kg mass:
1. Calculate the acceleration:
\[
a = \frac{F}{m} = \frac{12 \, \text{N}}{3 \, \text{kg}} = 4 \, \text{m/s}^2
\]
2. Calculate the change in velocity:
\[
\Delta v = a \cdot t = 4 \, \text{m/s}^2 \cdot 6 \, \text{s} = 24 \, \text{m/s}
\]
Therefore, the change in velocity of the mass would be \( 24 \, \text{m/s} \) given a force of \( 12 \, \text{N} \).
### Conclusion:
To fully determine the change in velocity, you will need the specific value of the force acting on the mass. You can then substitute that into the equations to find \( \Delta v \).