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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

12 m

D

16m

Text Solution

Verified by Experts

The correct Answer is:
b
Given , Displacement , `x = (t-2)^(2)`
Velocity , `v = (dx)/(dt) = 2 (t - 2) ms^(-1)`
Acceleration , `a = (dv)/(dt) = 2 m s^(-2)`
At `t = 0 , v = - 4 ms^(-1)`
At ` t = 2 , v = 0`
At `t = 4, v = 4 ms^(-1)`
Velocity - time graph is as shown in the figure.

Distance travelled = Area AOC + Area BCD
` = (1)/(2) (4 xx 2) +(1)/(2) (4xx2)`
` = 8 m`
The correct option is (b).
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