An object starts from rest and undergoes the following motion:

  1. It accelerates uniformly to a velocity of 20 m/s in the first 4 seconds.
  2. It then maintains this constant velocity for the next 2 seconds.
  3. 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:

  1. 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 s1=Area of triangle=12×base×height=12×4 s×20 m/s=40 ms_1 = \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \text{ s} \times 20 \text{ m/s} = 40 \text{ m}.
  2. 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 s2=Area of rectangle=base×height=2 s×20 m/s=40 ms_2 = \text{Area of rectangle} = \text{base} \times \text{height} = 2 \text{ s} \times 20 \text{ m/s} = 40 \text{ m}.
  3. 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 s3=Area of triangle=12×base×height=12×2 s×20 m/s=20 ms_3 = \text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 2 \text{ s} \times 20 \text{ m/s} = 20 \text{ m}. The total displacement is the sum of the displacements in each segment: Total Displacement = s1+s2+s3=40 m+40 m+20 m=100 ms_1 + s_2 + s_3 = 40 \text{ m} + 40 \text{ m} + 20 \text{ m} = 100 \text{ m}.