Question

the velocity of a particle moving on the x axis is given by v=x^2+ x where x is in meter and v is m/s and acceleration is 30 m/s^2 find x​

Answer 1

Answer :-

$\: \red{\boxed{\bf{ x \: = \frac{29}{2} } \: = 14.5}} \:$

To find :-

→ Find the value of x .

Formula used :-

$\star \: \boxed{ \bf{acceleration \: = \frac{dv}{dx} }} \\ \\ \star \: \boxed{ \bf{\frac{d}{dx} {x}^{n} = n \: {x}^{(n - 1)} } }$

Step - by - step explanation :-

Solution :-

Given that ,

• Acceleration = 30 m/s^{2}

According to the question,

$\implies \: \bf{ v \: = {x}^{2} + x}$

Now differentiating on both sides with respect to "x",

$\implies \: \bf{ \frac{dv}{dx} = 2x + 1} \: \: \: \: \: ......(1) \\ \\ \red{ \bf{ we \: know \: that \: }} \\ \\ \implies \: \bf{acceleration \: = \frac{dv}{dx} }$

and also given acceleration = 30 ,

$\implies \: \bf{ 30 = \frac{dv}{dx} }$

From equation (1),

$\implies \: \bf{ 30 = 2x + 1} \\ \\ \implies \: \bf{2x = 30 - 1} \\ \\ \implies \: \bf{ 2x = 29} \\ \\ \implies \: \red{\boxed{\bf{ x \: = \frac{29}{2} } \: = 14.5}}$