Question

If acceleration a = 3x2, where x is position then velocity is proportional to

Answer 1

Let acceleration be a and velocity be v and x be the position(displacment).

a=3x^2

now we know that a=dv/dx.

so dv/dx=3x^2.

so dv=(3x^2)(dx)

integrating both sides you get;

v=x^3 +c (since integration of x^n=[x^[n+1]/(n+1)] )

so v is directly proportional to x^3.