1. Tardigrade
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  4. The displacement of a particle is given by x = (t - 2)2 where x is in metres and t in seconds. The distance covered by the particle in first 4 seconds is

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Q. The displacement of a particle is given by $ x = (t - 2)^2 $ where $ x $ is in metres and $ t $ in seconds. The distance covered by the particle in first $ 4 $ seconds is

Motion in a Straight Line

Solution:

Given : $ x = (t - 2)^2 $
At $ t = 0 $ , $ x = x_0 = (0 - 2)^2 = 4 \,m $
$ t = 1\, s $ , $ x = x_1 = (1 - 2)^2 = 1 \,m $
$ t = 2\, s $ , $ x = x_2 = (2 - 2)^2 = 0\, m $
$ t = 3\, s $ , $ x = x_3 = (3 -2)^2= 1\,m $
$ t = 4\, s $ , $ x = x_4 = (4 - 2)^2 = 4 \,m $
The distance covered by the particle in $ 1^{st} $ second is $ D_1 = x_0 - x_1 = 3\, m $
The distance covered by the particle in II $ ^{nd} $ second is $ D_2 = x_1 - x_2 = 1 \,m $
Similarly, $ D_3= 1\,m $ , $ D_4 = 3\,m $
The distance covered by the particle in first 4 seconds is
$ D = D_1 + D_2 + D_3 + D_4 $
$ = 3\,m + 1\,m + 1\,m + 3\,m = 8\,m $