The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The accel

Question

The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The accelerationdisplacement graph of the bicycle's motion is best described by

Professor PC Thomas Classes · Answer

(d) : Given velocity - displacement graph Equation of line $A B$ \ $v=\frac{(50-10)}{(200-0)} 	imes(x-0)+10$\ $(0 \leq x \leq 200)$\ $\Rightarrow \quad v=\frac{40}{200} 	imes x+10$\ $\Rightarrow \quad v=\frac{x}{5}+10$ ...(i)\ Differentiate equation (i) w.r.t. $x$\ $\frac{d v}{d x}=\frac{1}{5}$ ...(ii)\ Acceleration, $a=\frac{d v}{d t}=\frac{d v}{d x} 	imes \frac{d x}{d t}=v \frac{d v}{d x}$\ $
a=\left(\frac{x}{5}+10ight) 	imes \frac{1}{5}
$
(Using (i) and (ii))\ $a=\left(\frac{x}{25}+2ight) \mathrm{m} \mathrm{s}^{-2}, \quad$ At $x=0, a=2 \mathrm{~m} \mathrm{~s}^{-2}$.\ It is straight line till $x=200$.
For $x>200, v=$ constant, $a=0$.
Therefore, most appropriate option will be (d).