The relation between time t and distance x for a moving body is given as t=m x2+n x, where m and n are constants. The retardation of the motion is: (When v stands for velocity)

Question

The relation between time t and distance x for a moving body is given as t=m x2+n x, where m and n are constants. The retardation of the motion is: (When v stands for velocity) (A) 2mv3 (B) 2mnv3 (C) 2nv3 (D) 2n2v3

Tardigrade Admin · Accepted Answer

t=m x2+n x (1/v)=(d t/d x)=2 m x+n v=(1/2 m x+n) (d v/d t)=-(2 m/(2 m x+n)2)((d x/d t)) a=-(2 m) v3

Q. The relation between time $t$ and distance $x$ for a moving body is given as $t = m x^{2} + n x$ , where $m$ and $n$ are constants. The retardation of the motion is: (When $v$ stands for velocity)

$2 m v^{3}$

$2 mn v^{3}$

$2 n v^{3}$

$2 n^{2} v^{3}$

$t = m x^{2} + n x$
$\frac{1}{v} = \frac{d t}{d x} = 2 m x + n$
$v = \frac{1}{2 m x + n}$
$\frac{d v}{d t} = - \frac{2 m}{( 2 m x + n ) ^{2}} (\frac{d x}{d t})$
$a = - (2 m) v^{3}$

Q. The relation between time t and distance x for a moving body is given as t=mx2+nx, where m and n are constants. The retardation of the motion is: (When v stands for velocity)

2mv3

2mnv3

2nv3

2n2v3