Determining the Distance Traveled by a Uniformly Accelerated Motorcycle
Understanding the motion of a motorcycle under uniform acceleration is a fundamental topic in physics. In this article, we delve into the calculation of the distance traveled by a motorcycle that starts from rest and moves with a uniform acceleration of 1 m/s2. Specifically, we will determine the distance traveled in the third second of its motion using the principles of uniformly accelerated motion.
Understanding Uniformly Accelerated Motion
When a motorcycle starts from rest and undergoes uniform acceleration, its velocity changes at a constant rate. If the initial velocity (u) is 0 (i.e., it starts from rest), and the acceleration (a) is 1 m/s2, the distance (s) traveled in a given time (t) can be calculated using the equation:
[ s ut frac{1}{2}at^2 ]Calculating the Distance Traveled in the Third Second
To find the distance traveled in the third second, we need to determine the total distance traveled in the first three seconds and then subtract the distance traveled in the first two seconds. This method allows us to isolate the distance traveled in the third second.
Distance Traveled in the First Three Seconds
Using the formula for distance traveled:
[ s_3 0t frac{1}{2} times 1 times 3^2 ][ s_3 frac{1}{2} times 9 4.5 , text{m} ]Distance Traveled in the First Two Seconds
Similarly, for the first two seconds:
[ s_2 0t frac{1}{2} times 1 times 2^2 ][ s_2 frac{1}{2} times 4 2 , text{m} ]Distance Traveled in the Third Second
The distance traveled in the third second is the difference between the distance traveled in the first three seconds and the distance traveled in the first two seconds:
[ s_{text{third second}} s_3 - s_2 ][ s_{text{third second}} 4.5 - 2 2.5 , text{m} ]This calculation shows that the motorcycle travels 2.5 meters in the third second of its motion.
Conclusion
Understanding the motion of a motorcycle under uniform acceleration is crucial for both theoretical and practical applications in mechanics. By using the principles of uniformly accelerated motion, we can accurately determine the distance traveled in any given second. This method can be applied to various real-world scenarios involving constant acceleration, such as vehicles in motion, projectiles, and more.
Whether you are a student, a physics enthusiast, or a professional interested in motion analysis, mastering the concepts of uniform acceleration can significantly enhance your problem-solving skills and deepen your understanding of physics.