Question

The acceleration of a particle moving along x axis is given by a=x³- 3x.it is at rest at x=1.find the velocity of the particle in m/s at x=3​

Answer 1

Answer:

The velocity of the particle at x=3 is 4 m/s

Explanation:

Given :

• The variation of acceleration with the displacement along x axis, $a=x^3-3x$
• The velocity of the particle is zero at x=1

Using Calculus we have

$a=v\dfrac{dv}{dx}\\x^3-3x=v\dfrac{dv}{dx}\\\\\dfrac{v^2}{2}=\dfrac{x^4}{4}-\dfrac{3x^2}{2}\\\\v^2=\dfrac{x^4}{2}-3x^2$

Now putting the value of v at x=1 and x=3

$v^2=\dfrac{(3^4-1^4)}{2}-3(3^2-1^2)\\v=4\ \rm m/s$

Hence the velocity is calculated.