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:

• A.
• B.
• C.
• D.

  

Answer 1

The correct option is A

The explanation for correct answer:-

Option (A)

1. As we know that $a=v(dv/dx)$.
2. The slope is constant and we know when the slope is constant acceleration is proportional to the velocity $\left(a\alpha v\right)$ from $(x=0to200m)$.
3. When slope $=0$ $acceleration=0$ from $x=200to400m$
4. $$\begin{gathered} v=mx+C \\ v=\frac{1}{5}x+10 \\ a=v\frac{dv}{dx}=\left(\frac{1}{5}x+10\right)\left(\frac{1}{5}\right) \\ a=\frac{x}{25}+2 \end{gathered}$$
5. Straight line till $x=200$
6. For $x>200$
7. $v=cons\tan t$
8. $a=0$

The figure is shown below by the above condition:

Hence, the correct answer is option (A).