Understanding the Problem
* Constant Velocity: If the object is moving at a constant velocity (no acceleration), then the distance covered in the last second is the same as the distance covered in any other second.
* Acceleration: If the object is accelerating, the distance covered in each second will be different.
Required Information
To determine the distance covered in the last second, you need at least one of the following:
1. Initial Velocity (v₀): The speed of the object at the beginning of its motion.
2. Final Velocity (v): The speed of the object at the end of its motion.
3. Acceleration (a): The rate at which the object's velocity changes.
4. Total Time (t): The duration of the object's motion.
Calculations
Here's how to calculate the distance covered in the last second depending on the information you have:
* Constant Velocity:
* Distance = Velocity x Time
* In this case, time is 1 second.
* Uniform Acceleration:
* You can use the following kinematic equation:
* d = v₀t + (1/2)at²
* Where:
* d = distance
* v₀ = initial velocity
* t = time (1 second in this case)
* a = acceleration
* To find the distance in the last second, calculate the total distance traveled over the entire time and then subtract the distance traveled in the first (t-1) seconds.
Example
Let's say an object starts from rest (v₀ = 0 m/s) and accelerates at 2 m/s². We want to find the distance covered in the last second of a 5-second journey.
1. Total Distance (5 seconds):
* d = (0 m/s)(5 s) + (1/2)(2 m/s²)(5 s)² = 25 meters
2. Distance in the first 4 seconds:
* d = (0 m/s)(4 s) + (1/2)(2 m/s²)(4 s)² = 16 meters
3. Distance in the last second:
* 25 meters - 16 meters = 9 meters
In Conclusion
To find the distance covered in the last second of an object's motion, you need to know the object's initial velocity, final velocity, acceleration, or total time. With this information, you can use appropriate kinematic equations to calculate the distance.
