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 m to x=12 m 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 m to x=12 m is (A) 16/3 sec (B) 10 sec (C) 8 sec (D) 12 sec

Tardigrade Admin · Accepted Answer

First find relation between v and x (1/v)=(3 x/16)-(1/4) ⇒ (d t/d x)=(3 x/16)-(1/4) ⇒ ∫ limitst1t2 d t=∫ limits412((3 x/16)-(1/4)) d x Solve to get t2-t1=10 s

Q. 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 $x = 4 m$ to $x = 12 m$ is

16/3 sec

10 sec

8 sec

12 sec

First find relation between $v$ and $x$
$\frac{1}{v} = \frac{3 x}{16} - \frac{1}{4}$
$\Rightarrow \frac{d t}{d x} = \frac{3 x}{16} - \frac{1}{4}$
$\Rightarrow t_{1} \int t_{2} d t = 4 \int 12 (\frac{3 x}{16} - \frac{1}{4}) d x$
Solve to get $t_{2} - t_{1} = 10 s$

Q. 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=4m to x=12m is