The displacement of a particle is given by $x = (t-2)^2$. The distance covered by the particle in th

Question

The displacement of a particle is given by $x = (t-2)^2$. The distance covered by the particle in the first $4$ seconds is:

Professor PC Thomas Classes · Answer

Velocity $v = \frac{dx}{dt} = 2(t-2)$. The velocity is zero at $t = 2	ext{ s}$. For $t = 0$ to $2	ext{ s}$, the particle moves from $x = 4	ext{ m}$ to $x = 0	ext{ m}$ (Distance $= 4	ext{ m}$). For $t = 2$ to $4	ext{ s}$, the particle moves from $x = 0	ext{ m}$ to $x = 4	ext{ m}$ (Distance $= 4	ext{ m}$). Total distance $= 4 + 4 = 8	ext{ m}$. (Note that the displacement is $0$).