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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

4m

B

8m

C

12m

D

16m

Text Solution

Verified by Experts

The correct Answer is:
B
Given `x = (t - 2)^2`
`v = (dx)/(dt) = (d)/(dt) (t -2)^2 = 2(t - 2) m//s`
`a = (dv)/(dt) = (d)/(dt) [2(t-2)]`
` = 2[1-0]=2m//s^2`
when t = 0 , v = -4m/s
t = 2s , v = 0m/s
t = 4s, v = 4m/s

v-t graph is shown in adjacent diagram
Distance travelled = graph of the area
= Area OAC + Area ABD
`= (4xx2)/(2) + 1/2 xx 2 xx 4 = 8m`
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