Question

The displacement of a particle is given by `x=(t-2)^(2)` where x is in meter and t in second. The distance covered by the particle in first 3 seconds is
A. 4 m
B. 8 m
C. 12 m
D. 16 m

Answer 1

Correct Answer - D
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] = 2 m//s^(2)`
When `t = 0, v = - 4 m//s`
`t = 2s, v = 0 m//s`
`t = 4s, v = 4 m//s`
`v -t` graph is shown in adjacent diagram,
Distance travelled `=` area of the graph
`=` area of `OAC +` area ABD
`= (4 xx 2)/(2) + 1/2 xx 2 xx 4 = 8m`