Question

The potential energy of $4kg$ particle free to move along the $x$axis is given by $u\left(X\right)=\frac{x^3}{3}-\frac{5x^2}{2}+6x+3$.Total mechanical energy of the paticle is $17J$. Then the maximum kinetic energy is

• A. $10J$
• B. $2J$
• C. $9.5J$
• D. $0.5J$

Answer 1

The correct option is C $9.5J$

To find minimum potential energy we can differentiate u(X) w.r.t x and find the x for which u(X) is minimum by making its derivative = 0.

$\frac{d\left(u\right(x\left)\right)}{dx}=x^2-5x+6=0$

from here x=2,3

But we get minimum potential energy at x=3 which is equal to 7.5 J

So, maximum potential energy =17-7.5=9.5J