Question:
The velocity-displacement graph describing the motion of a bicycle is shown in the figure
The acceleration-displacement graph of the bicycle's motion is best described by :
Correct Option: 1
Solution:
For $0 \leq x \leq 200$
$\mathrm{v}=\mathrm{mx}+\mathrm{C}$
$v=\frac{1}{5} x+10$
$a=\frac{v d v}{d x}=\left(\frac{x}{5}+10\right)\left(\frac{1}{5}\right)$
$\mathrm{a}=\frac{\mathrm{x}}{25}+2 \Rightarrow$ Straight line till $\mathrm{x}=200$
for $x>200$
$\mathrm{v}=\mathrm{constant}$
$\Rightarrow a=0$
Hence most approriate option will be (1), otherwise it would be BONUS.