Understanding Kinematics: Solving for Final Velocity in Uniformly Accelerated Motion
In the field of physics, kinematics often deals with the study of motion without considering the forces that cause it. If you are trying to determine the final velocity of an object that is accelerating uniformly, the equation of motion becomes a powerful tool. This article will guide you through solving a real-world problem step-by-step, helping you understand and apply the relevant equations of motion.
Problem Statement
A motorcycle traveling at 17 meters per second (m/s) accelerates at a constant rate of 4.0 meters per second squared (m/s2) over a distance of 45 meters (m). What is its final velocity?
Solving the Problem Using Kinematic Equations
To solve this problem, we will use the second equation of motion, which is:
V2 U2 2as
Where:
V Final velocity (m/s) U Initial velocity (m/s) a Acceleration (m/s2) s Distance (m)Step-by-Step Solution
Identify the given variables: Initial velocity, U 17 m/s Acceleration, a 4.0 m/s2 Distance, s 45 m Substitute the given values into the equation:V2 172 2 × 4 × 453. Calculate the value:
V2 289 360V2 6494. Take the square root:
V √649 ≈ 25.47 m/s
General Approach
When solving kinematic problems, it's crucial to have a systematic approach. Here is a general approach to solving such problems:
Identify the known variables: U, a, s, v (one of them will be unknown). Select the appropriate equation: Use V2 U2 2as if you have U, a, and s but not v. Substitute the known values: Plug the known values into the equation. Solve for the unknown variable: Rearrange the equation if necessary and solve for the unknown.Key Equations in Kinematics
V U at S Ut (1/2)at2 S (V2 - U2) / (2a) S (U V) t / 2When solving kinematic problems, it's essential to be mindful of sign conventions. Choose a positive direction and stick to it throughout the problem. Additionally, these equations are only applicable if the acceleration is constant. If the acceleration is not constant, further calculus techniques, such as integration, may be necessary.
Conclusion
By understanding and applying the kinematic equations, you can solve a wide range of problems related to uniformly accelerated motion. Whether you are calculating final velocity, displacement, time, or acceleration, these equations are your go-to tools in physics. Practice using them in different scenarios to enhance your problem-solving skills.