Physics Problem: Calculating Velocity from Force and Time

This problem involves calculating the final velocity of an object after a force is applied for a specific duration, starting from rest.

Applying Physics Principles

We need to use two fundamental physics principles:

• Newton's Second Law of Motion: \(F = ma\), where \(F\) is force, \(m\) is mass, and \(a\) is acceleration.
• A kinematic equation: \(v = u + at\), where \(v\) is final velocity, \(u\) is initial velocity, \(a\) is acceleration, and \(t\) is time.

Step-by-Step Solution

1. Calculate Acceleration:

   Given: Mass (\(m\)) = 3 kg, Force (\(F\)) = 6 N. Using Newton's Second Law, we find acceleration (\(a\)).

   \(a = \frac{F}{m}\)

   \(a = \frac{6 \, \text{N}}{3 \, \text{kg}} = 2 \, \text{m/s}^2\)

2. Calculate Final Velocity:

   Given: Initial velocity (\(u\)) = 0 m/s (since the object is at rest), acceleration (\(a\)) = 2 m/s\(^2\), time (\(t\)) = 3 s. Using the kinematic equation:

   \(v = u + at\)

   \(v = 0 \, \text{m/s} + (2 \, \text{m/s}^2)(3 \, \text{s})\)

   \(v = 0 + 6 \, \text{m/s}\)

   \(v = 6 \, \text{m/s}\)

The velocity acquired by the object is 6 m/s.