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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:
A
Here, ` x = (t - 2) ^2 , velcity , ` v = 9dx0/(dt) = 2 ( t-2) m//s , acceleration, ` a= (dv) /(dt0 =2 ms^(-2)` (i.e. uniform)`
When ` t=0 , v =- m//s , t = 2 s , v-0`
` t= 4 s, v = 4 m//s`.
Velocity 9v) -time (t) graph of this motion is as shown in Fig. 2 (EP) , 4 `
Distance travelled = area ` AOB = ( 4 xx2 )/2 + ( 4 xx 2)/2 = 8m`
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