 Find the acceleration of a particle of mass mand velocity vwhen it is acted upon by the con
stant force F,where F is parallel to v.

To find the acceleration of a particle of mass \( m \) and velocity \( v \), when it is acted upon by a constant force \( F \) (where \( F \) is parallel to \( v \)), we can use Newton's second law of motion. 

Newton's second law states:

\[
\mathbf{F} = m\mathbf{a}
\]

where:
- \( \mathbf{F} \) is the force applied to the particle,
- \( m \) is the mass of the particle, and
- \( \mathbf{a} \) is the acceleration of the particle.

Since the force \( F \) is parallel to the velocity \( v \), the acceleration \( \mathbf{a} \) will also be in the same direction as the force. Therefore, we can express the acceleration as:

\[
\mathbf{a} = \frac{\mathbf{F}}{m}
\]

So, the magnitude of the acceleration \( a \) is:

\[
a = \frac{F}{m}
\]

### Summary:
- **Acceleration** \( \mathbf{a} = \frac{\mathbf{F}}{m} \).
- Since \( F \) is parallel to \( v \), \( \mathbf{a} \) will also be in the same direction as \( \mathbf{F} \).

Would you like further details or have any questions?

### Related Questions:
1. What happens to the acceleration if the force is not parallel to the velocity?
2. How does the acceleration change if the mass of the particle doubles?
3. What is the relationship between force, mass, and acceleration if the force is at an angle to the velocity?
4. How does Newton's second law apply to rotational motion?
5. What are the implications of varying mass on acceleration for a non-constant force?

**Tip:** Remember that force and acceleration are vectors, meaning they have both magnitude and direction.

Learn how to find the acceleration of a particle given its mass \( m \), velocity \( v \), and a constant force \( F \) parallel to the velocity. Understand Newton's second law of motion and the relationship between force, mass, and acceleration. Suitable for high school students studying physics.

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