The velocity of a particle moving on the x-axis is given by v=x2+x, where v is in m / s and x is in m. Find its acceleration (in m / s 2 ) when passing through the point x=2 m.

Question

The velocity of a particle moving on the x-axis is given by v=x2+x, where v is in m / s and x is in m. Find its acceleration (in m / s 2 ) when passing through the point x=2 m. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

v=x2+x ⇒ (d v/d t)=2 x (d x/d t)+(d x/d t) ⇒ a=(2 x+1) v =(2 x+1)(x2+x) ∴ When x=2 m, a=(2 × 2+1)(22+2) =5 × 6=30 m / s 2

Q. The velocity of a particle moving on the $x$ -axis is given by $v = x^{2} + x$ , where $v$ is in $m / s$ and $x$ is in $m$ . Find its acceleration (in $m / s^{2}$ ) when passing through the point $x = 2 m$ .

$v = x^{2} + x$
$\Rightarrow \frac{d v}{d t} = 2 x \frac{d x}{d t} + \frac{d x}{d t}$
$\Rightarrow a = (2 x + 1) v$
$= (2 x + 1) (x^{2} + x)$
$∴$ When $x = 2 m$ ,
$a = (2 \times 2 + 1) (2^{2} + 2)$
$= 5 \times 6 = 30 m / s^{2}$

Q. The velocity of a particle moving on the x-axis is given by v=x2+x, where v is in m/s and x is in m. Find its acceleration (in m/s2 ) when passing through the point x=2m.

v=x2+x ⇒dtdv​=2xdtdx​+dtdx​ ⇒a=(2x+1)v =(2x+1)(x2+x) ∴ When x=2m, a=(2×2+1)(22+2) =5×6=30m/s2

Q. The velocity of a particle moving on the $x$ -axis is given by $v = x^{2} + x$ , where $v$ is in $m / s$ and $x$ is in $m$ . Find its acceleration (in $m / s^{2}$ ) when passing through the point $x = 2 m$ .

$v = x^{2} + x$
$\Rightarrow \frac{d v}{d t} = 2 x \frac{d x}{d t} + \frac{d x}{d t}$
$\Rightarrow a = (2 x + 1) v$
$= (2 x + 1) (x^{2} + x)$
$∴$ When $x = 2 m$ ,
$a = (2 \times 2 + 1) (2^{2} + 2)$
$= 5 \times 6 = 30 m / s^{2}$