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

Options

A. 4m
B. 8m
C. 12m
D. 16m

Answer

B

Explanation

Given, `x = (t-2) ^(2)`
Velocity, `v = (dx)/(dt) = (d)/(dt)(t-2) ^(2) = 2 (t -2) m//s`
Acceleration,` a = (dv)/(dt) = (d)/(dt) [2 (t -2)]`
`=2 [1-0]=2m//s^(2)`
When,` t =0 implies v=- 4m//s`
`t = 2s implies v =0 m//s`
`t = 4s implies v = 4 m//s`

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