Understanding Force, Mass, and Motion

This question asks us to determine how a body will move when a specific force is applied to it, given its mass and the ability to move freely. This scenario directly relates to Newton's laws of motion, specifically Newton's Second Law, which describes the relationship between force, mass, and acceleration.

Applying 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 upon it and inversely proportional to its mass. The direction of the acceleration is in the same direction as the net force. Mathematically, this is expressed as:

$$\mathbf{F} = m\mathbf{a}$$

Where:

• $\mathbf{F}$ is the net force acting on the object (in Newtons, N)
• $m$ is the mass of the object (in kilograms, kg)
• $\mathbf{a}$ is the acceleration of the object (in meters per second squared, m/s²)

Calculating the Acceleration

We are given the following information:

• Force ($\mathbf{F}$) = 10 N
• Mass ($m$) = 10 kg

We need to find the acceleration ($\mathbf{a}$). We can rearrange Newton's Second Law formula to solve for acceleration:

$$\mathbf{a} = \frac{\mathbf{F}}{m}$$

Now, let's substitute the given values into the formula:

$$\mathbf{a} = \frac{10 \text{ N}}{10 \text{ kg}}$$

Since 1 N = 1 kg⋅m/s², the units work out correctly:

$$\mathbf{a} = \frac{10 \text{ kg} \cdot \text{m/s}^2}{10 \text{ kg}}$$

$$\mathbf{a} = 1 \text{ m/s}^2$$

So, the body will move with an acceleration of 1 m/s².

Analyzing the Given Statements

Let's examine each statement based on our calculation:

1. The body moves with a speed of 1 km/s
2. The body moves with an acceleration of 10 ms ^-2
3. The body moves with an acceleration of 1 ms ^-2
4. The body moves with a speed of 1 m/s

Our calculation shows the acceleration is 1 m/s². Speed is the rate of change of distance, while acceleration is the rate of change of velocity (which includes speed and direction). A force causes acceleration, which in turn changes the velocity (and thus speed). A constant force results in constant acceleration, not necessarily a constant speed. The speed will increase over time due to the acceleration.

• Statement 1 mentions speed (1 km/s). This cannot be directly determined from just the force and mass; it depends on how long the force acts.
• Statement 2 mentions acceleration of 10 m/s². Our calculation yielded 1 m/s², so this statement is incorrect.
• Statement 3 mentions acceleration of 1 m/s². This matches our calculated acceleration.
• Statement 4 mentions speed (1 m/s). Like Statement 1, speed is not directly given by force and mass; it is a consequence of the acceleration over time. The body starts from rest (implicitly) and its speed will increase.

Therefore, the only statement that correctly describes the immediate effect of the 10 N force on the 10 kg mass is the one about its acceleration.

Conclusion

Based on Newton's Second Law of Motion, a force of 10 N acting on a mass of 10 kg will cause an acceleration. The magnitude of this acceleration is calculated to be 1 m/s². Therefore, the statement that the body moves with an acceleration of 1 m/s² is the correct one.

Revision Table: Key Concepts

Additional Information: Force, Mass, and Acceleration

Newton's Second Law is a fundamental principle in physics. It quantifies the effect of a force on an object's motion. When a force acts on an object, it doesn't cause a sudden change in speed unless the force is impulsive. Instead, it causes a constant change in velocity over time, which is acceleration. The amount of acceleration depends on both the magnitude of the force and the mass of the object. A larger force produces more acceleration, while a larger mass resists acceleration, requiring more force to achieve the same acceleration.

It's important not to confuse acceleration with velocity or speed. Velocity is a measure of how fast an object is moving and in what direction. Speed is the magnitude of velocity. Acceleration is the rate at which velocity changes. If an object has constant acceleration, its velocity changes by the same amount each second. For example, an acceleration of 1 m/s² means the object's velocity increases by 1 m/s every second, assuming the force is constant and in the direction of motion and there are no other significant forces like friction.