Graph of $(1 / v)$ vs $x$ for a particle under motion is as shown, where $v$ is velocity and $x$ is

Question

Graph of $(1 / v)$ vs $x$ for a particle under motion is as shown, where $v$ is velocity and $x$ is position. The time taken by particle to move from $x=4 \mathrm{~m}$ to $x=12 \mathrm{~m}$ is

Professor PC Thomas Classes · Answer

(b) : First, find relation between $v$ and $x$. $ \  \frac{1}{v}=\frac{3 x}{16}-\frac{1}{4} \Rightarrow \frac{d t}{d x}=\frac{3 x}{16}-\frac{1}{4} \Rightarrow \int_{t_1}^{t_2} d t=\int_4^{12}\left(\frac{3 x}{16}-\frac{1}{4}ight) d x $ \ Solve to get $t_2-t_1=10 \mathrm{~s}$.