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The displacement of a particle is moving...

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

A

4 m

B

8 m

C

12 m

D

16 m

Text Solution

Verified by Experts

The correct Answer is:
(b)
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 bt 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
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