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.

Options

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

Answer

B

Explanation

given `x = (t - )^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 = 2 s, v = 0 m//s`
`t = 4 s , v = 4 m//s`
`v-t` graph is shown adjacent diagram.
Distance travelled = area of the graph
= area `OAC + area ABD`
=`(4 xx 2)/(2) + (1)/(2) xx 2 xx 4 = 8 m`.