A constant force is applied to an object, causing the object to accelerate at 10 m/s². What will the acceleration be if the force is halved?

Verified step by step guidance

1. Identify the relationship between force and acceleration using Newton's Second Law of Motion: $F=ma$, where $F$ is the force, $m$ is the mass, and $a$ is the acceleration.
2. Rearrange the formula to solve for acceleration: $a=\frac{F}{m}$. This shows that acceleration is directly proportional to the force applied, assuming the mass remains constant.
3. Understand the problem: The initial acceleration is given as 10 m/s² when a certain force is applied. If the force is halved, the new force becomes $\frac{1}{2}F$.
4. Substitute the halved force into the formula for acceleration: $\mathrm{a\text{'}}=\frac{\frac{1}{2}F}{m}$. Simplify this to get $\mathrm{a\text{'}}=\frac{1}{2}a$, where $\mathrm{a\text{'}}$ is the new acceleration.
5. Finally, use the given initial acceleration of 10 m/s² to determine the proportional change. The new acceleration will be half of the initial acceleration, as derived in the previous step.

Key Concepts

Newton's Second Law of Motion

Newton's Second Law states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass. This relationship is expressed by the formula F = ma, where F is the net force, m is the mass, and a is the acceleration. Understanding this law is crucial for analyzing how changes in force affect acceleration.

Force and Acceleration Relationship

The relationship between force and acceleration indicates that if the force applied to an object is changed, the acceleration will also change accordingly, assuming the mass remains constant. Specifically, if the force is halved, the acceleration will also be halved, demonstrating the direct proportionality between force and acceleration as described by Newton's Second Law.

Mass of the Object

The mass of an object is a measure of its resistance to acceleration when a force is applied. In the context of Newton's Second Law, mass remains constant unless specified otherwise. Therefore, when analyzing the effect of halving the force on acceleration, the mass must be considered constant to accurately determine the new acceleration value.