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

The displacement of a particle is given by x = (t-2)^(2)where x is in

1.	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
Answer» 4m 8m 12m 16m Solution :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) + 1/2xx 2 xx 4 =8m`