A particle is moving with speed n = b √x along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0).

Question

A particle is moving with speed n = b √x along positive x-axis. Calculate the speed of the particle at time t = τ (assume that the particle is at origin at t = 0). (A) (b2 τ/4) (B) (b2 τ/2) (C) b2 τ (D)  (b2 τ/1)

Tardigrade Admin · Accepted Answer

v = b√x (dv/dt) = (b/2√x) (dx/dt) a = (bv/2√x) a = (b(b√x)/2√x) (dv/dt) = a = (b2/2) v = (b2/2) τ

Q. A particle is moving with speed $n = b x$ along positive x-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ ).

$\frac{b ^{2} τ}{4}$

$\frac{b ^{2} τ}{2}$

$b^{2} τ$

$\frac{b ^{2} τ}{1}$

$\frac{b ^{2} τ}{2}$

$v = b x$
$\frac{d v}{d t} = \frac{b}{2 x} \frac{d x}{d t}$
$a = \frac{b v}{2 x}$
$a = \frac{b ( b x )}{2 x}$
$\frac{d v}{d t} = a = \frac{b ^{2}}{2}$
$v = \frac{b ^{2}}{2} τ$

Q. A particle is moving with speed n=bx​ along positive x-axis. Calculate the speed of the particle at time t=τ (assume that the particle is at origin at t=0).

4b2τ​

2b2τ​

b2τ

1b2τ​

2​b2τ​

v=bx​ dtdv​=2x​b​dtdx​ a=2x​bv​ a=2x​b(bx​)​ dtdv​=a=2b2​ v=2b2​τ

Q. A particle is moving with speed $n = b x$ along positive x-axis. Calculate the speed of the particle at time $t = τ$ (assume that the particle is at origin at $t = 0$ ).

$\frac{b ^{2} τ}{4}$

$\frac{b ^{2} τ}{2}$

$b^{2} τ$

$\frac{b ^{2} τ}{1}$

$\frac{b ^{2} τ}{2}$

$v = b x$
$\frac{d v}{d t} = \frac{b}{2 x} \frac{d x}{d t}$
$a = \frac{b v}{2 x}$
$a = \frac{b ( b x )}{2 x}$
$\frac{d v}{d t} = a = \frac{b ^{2}}{2}$
$v = \frac{b ^{2}}{2} τ$