A bird flies for 4 s with a velocity of |t–2|m/s in a straight line, where t is time in seconds. It covers a distance of

u = ∣t−2∣

Velocity = |t - 2|

Time, t =4 s

at t = 0, u = 2 m/sec

t = 2, u = 0 m/sec

t = 4 ,u = 2 m/sec

Between time t = 0 sec and t = 2 sec 

$$\begin{gathered} a=\frac{0-2}{2}=-1m/se{c}^2 \\ {s}_1=ut+\frac{1}{2}a{t}^2 \\ {s}_1=2\times 2+\frac{1}{2}\times (-1)\times 4=2 \end{gathered}$$

Between time t = 2 sec and t = 4sec

$$\begin{gathered} a=\frac{2-0}{2}=1m/se{c}^2 \\ {s}_2=\frac{1}{2}\times 1\times 4=2 \end{gathered}$$

Then the total distance = S₁ + S₂ = 2m + 2m = 4m.