Calculating Final Velocity with Force and Time

This problem asks us to find the final velocity of a body when a constant force acts on it for a specific duration. We are given the initial mass, initial velocity, the magnitude of the applied force, and the time duration the force acts.

To solve this, we can use the principles of dynamics, specifically Newton's Second Law of Motion and the equations of uniformly accelerated motion.

Understanding the Given Information

Let's list the values provided in the question:

• Mass of the body, \(m = 10 \, \text{kg}\)
• Initial velocity of the body, \(u = 1 \, \text{m/s}\)
• Force acting on the body, \(F = 50 \, \text{N}\)
• Time duration for which the force acts, \(t = 2 \, \text{seconds}\)

Calculating Acceleration

When a force acts on a body, it causes the body to accelerate. Newton's Second Law of Motion gives the relationship between force, mass, and acceleration:

\[ F = ma \]

Where \(F\) is the force, \(m\) is the mass, and \(a\) is the acceleration. We can rearrange this formula to find the acceleration:

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

Let's plug in the given values:

\[ a = \frac{50 \, \text{N}}{10 \, \text{kg}} \]

\[ a = 5 \, \text{m/s}^2 \]

So, the acceleration of the body due to the applied force is \(5 \, \text{m/s}^2\).

Calculating Final Velocity

Now that we have the acceleration, initial velocity, and time, we can find the final velocity using one of the standard equations of motion for constant acceleration. The relevant equation here is:

\[ v = u + at \]

Where \(v\) is the final velocity, \(u\) is the initial velocity, \(a\) is the acceleration, and \(t\) is the time.

Let's substitute the known values into this equation:

\[ v = (1 \, \text{m/s}) + (5 \, \text{m/s}^2)(2 \, \text{s}) \]

First, calculate the product of acceleration and time:

\[ at = (5 \, \text{m/s}^2)(2 \, \text{s}) = 10 \, \text{m/s} \]

Now, add this to the initial velocity:

\[ v = 1 \, \text{m/s} + 10 \, \text{m/s} \]

\[ v = 11 \, \text{m/s} \]

The final velocity of the body after 2 seconds is \(11 \, \text{m/s}\).

Summary of Calculation

The calculation shows that applying a force of 50 N for 2 seconds to a 10 kg mass initially moving at 1 m/s increases its velocity by 10 m/s, resulting in a final velocity of 11 m/s.