An object starts from rest and undergoes the following motion:
- It accelerates uniformly to a velocity of 20 m/s in the first 4 seconds.
- It then maintains this constant velocity for the next 2 seconds.
- Finally, it decelerates uniformly to rest in another 2 seconds. What is the total displacement of the object during its entire motion?
Options
Option A
80 m
Option B is correct
100 m
Option C
120 m
Option D
140 m
Explanation
The total displacement of the object can be calculated by finding the area under its velocity-time graph. We can divide the motion into three segments:
- Segment 1 (0 to 4 seconds): The object accelerates uniformly from rest (0 m/s) to 20 m/s. This forms a triangle on the velocity-time graph. Displacement .
- Segment 2 (4 to 6 seconds): The object moves at a constant velocity of 20 m/s for 2 seconds. This forms a rectangle on the velocity-time graph. Displacement .
- Segment 3 (6 to 8 seconds): The object decelerates uniformly from 20 m/s to rest (0 m/s) in 2 seconds. This forms another triangle on the velocity-time graph. Displacement . The total displacement is the sum of the displacements in each segment: Total Displacement = .