Calculating Final Velocity Under Constant Force: A Comprehensive Guide

Understanding the relationship between force, velocity, and time in motion is crucial in many fields, including engineering, physics, and everyday problem-solving scenarios. One of the fundamental principles that help us solve such problems is Newton's Second Law of Motion. This law helps us determine the final velocity of an object when a constant force is applied to it over a given period. In this article, we will walk through a step-by-step example to find the final velocity of a vehicle under these conditions.

Introduction to the Problem

A vehicle of mass 1500 kg is moving with an initial velocity of 15 m/s. A force of 1000 N is applied in the direction of its motion. We will use Newton's Second Law and the equations of motion to find the vehicle's velocity after 15 seconds. This example will highlight the application of physics principles in real-world scenarios, providing valuable insights into the dynamics of motion.

Step-by-Step Solution

Step 1: Calculate the Acceleration

According to Newton's Second Law of Motion, the relationship between force, mass, and acceleration is:

F m · a

Where:

F is the force applied (1000 N) m is the mass of the vehicle (1500 kg) a is the acceleration

Rearranging the equation to solve for acceleration:

a F/m

Substituting the given values:

a 1000 N / 1500 kg 0.67 m/s2

Average acceleration 0.67 m/s2

Step 2: Calculate the Final Velocity

To find the final velocity, we can use the equation:

v u a · t

Where:

v is the final velocity u is the initial velocity (15 m/s) a is the acceleration (0.67 m/s2) t is the time (15 s)

Substituting the known values:

v 15 m/s 0.67 m/s2 · 15 s

First, calculate the acceleration component:

0.67 m/s2 · 15 s 10.05 m/s

Now add this to the initial velocity:

v 15 m/s 10.05 m/s 25.05 m/s

The final velocity after 15 seconds is approximately 25 m/s.

Conclusion

The final velocity of the vehicle after 15 seconds, given the initial conditions, is 25 m/s. This example demonstrates the application of fundamental physics principles to solve practical problems related to motion and force. Understanding these concepts is essential for students, professionals, and enthusiasts interested in the dynamics of moving objects.

Additional Insights

Impulse and momentum are also closely related to this problem. The impulse imparted by the force is equal to the change in momentum:

Impulse 1000 N · 15 s 15000 N·s

Change in momentum 15000 N·s / 1500 kg 10 m/s

This confirms that the change in velocity is also 10 m/s, leading to the same final velocity of 25 m/s.