Question

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

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

Answer: (B)

Here, $v=|t-2|m{s}^{-1}$
$v=t-2,$ when $t>2s$
$v=2-t,$ when $t<2s$
$\therefore a=\frac{dv}{dt}=1m{s}^{-2}$ when $t>2s$
$a=-1m{s}^{-2}$ when $t<2s$

In the direction of motion from $A$ to $C$, bee decelerates but for $C$ to $B$, bee accelerates.
Let $AC=s_1,BC=s_2$
$u_A=2m{s}^{-1},t=0$
$200100,(m)300m_{rel}=+=u_C=0at$
$\therefore s_1=\left(\frac{u_A+u_C}{2}\right)t_1$
$s_2=\left(\frac{u_C+u_B}{2}\right)t_2$
$\therefore s=s_1+s_2=\left(\frac{2+0}{2}\right)2+\left(\frac{0+2}{2}\right)2=4m$