Question

The velocity-time graph of a moving body is given below in figure. Find displacement in each part AB, BC, CD, and total displacement.

Answer 1

We know, area under the velocity time graph represents displacement covered.
For part AB:
Displacement is equal to the area of triangle shaded during interval 0 to 4 s.

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑣 − 𝑡 𝑔𝑟𝑎𝑝ℎ
$=\frac{1}{2}\times 30m{s}^{-1}\times 4s=60$ m

For part BC: Displacement will be equal to the area of shaded rectangle during interval 4 𝑠 𝑡𝑜 8 𝑠.

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑣 − 𝑡 𝑔𝑟𝑎𝑝ℎ
$=30m{s}^{-1}\times 4s=120$ m

For part CD: Displacement will be equal to the area of shaded triangle during interval 8 𝑠 𝑡𝑜 10 𝑠

𝐷𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡 = 𝐴𝑟𝑒𝑎 𝑢𝑛𝑑𝑒𝑟 𝑣 − 𝑡 𝑔𝑟𝑎𝑝ℎ
$=\frac{1}{2}\times 30m{s}^{-1}\times 2s=30$m

Total displacement = Displacement of part AB + Displacement of part BC + Displacement of part CD = 60 + 120 + 30 = 210 m
Hence, the total displacement is $210$ m.