A bee flies a line from a point A to another point B in 4 s with a velocity of $|t-2|m{s}^{-1}.$ The distance between A and B in  metre is

Here, $v=|t-2|m{s}^{-1}$

v = t -2,when t > 2 s

 v = 2 -t ,when t < 2 s

$\therefore a=\frac{dv}{dt}=1m{s}^{-2}whent>2s$

$a=-1m{s}^{2}whent<2s$

In the direction of motion from A to C, bee decelerates but for C to B, bee accelerates.

Let $AC=s_1,BC=s_2$

$u_A=2m{s}^{-1},t=0$

$u_C=0at,t=4s$

$s_1=\left(\frac{u_A+u_C}{2}\right)t_1$

$s_2=\left(\frac{u_C+u_B}{2}\right)t_2$

$\therefore s=s_1+s_2=\left(\frac{2+0}{2}\right)2+\left(\frac{0+2}{2}\right)2=4m$