Understanding Uniform Acceleration through Distance and Velocity Calculations
The concept of uniform acceleration is fundamental in physics, particularly when analyzing the motion of objects starting from rest under constant acceleration. This article will delve into the mathematical process to determine the final velocity of an object given information about its distance traveled during any specific second of its motion.
Problem and Solution
Consider the problem where a body starts from rest with a uniform acceleration and travels 18 meters during the 3rd second. Our objective is to find the velocity of the body at the end of the 8th second.
Step 1: Finding the Acceleration
To begin, we will use the formula to determine the distance traveled during the nth second of motion:
dn u
Given that the body starts from rest, u 0, the formula simplifies to:
dn
Since the object travels 18 meters during the 3rd second (n 3), we can substitute the values:
18
18
18
18
a 2
Step 2: Calculating the Final Velocity
The final velocity at the end of t seconds can be calculated using the formula:
v u at
Given that the initial velocity u 0, we have:
v 0 a times; 8
v 7.2 times; 8 57.6 m/s
Conclusion
The velocity of the body at the end of the 8th second is 57.6 m/s.
Additional Insights
The provided solution incorrectly applied the distance formula. The correct approach is to use the provided information on distance traveled during the 3rd second to derive the acceleration and then use the velocity formula at the end of the 8th second.
Alternative Approach
Another method to solve this problem is by using the SUVAT equations (displacement, velocity, time, acceleration, and initial velocity). The distance formula is:
xt x0 v0t 2
After 2 seconds, the position is:
x2 x0 v0 times; 2 2
After 3 seconds:
x3 x0 v0 times; 3 2
The distance traveled during the 3rd second is:
x3 - x2 18 meters
Substituting the values:
v0 times; 5
Since the object starts from rest, v0 0, we get:
Thus, a 2
The velocity at the end of the 8th second is:
v at 7.2 times; 8 57.6 m/s
Further Reading and Resources
For additional support or to discuss similar problems, you can visit Physics Forums - The Fusion of Science and Community, a community forum dedicated to the exploration of physics.
Conclusion
The velocity of the object at the end of the 8th second, given the initial conditions of starting from rest with a uniform acceleration and traveling 18 meters during the 3rd second, is 57.6 m/s. This problem showcases the application of basic kinematic equations to solve real-world physics problems.