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 particle 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 $9.5J$

when potential energy is minimum ,kinetic energy is maximum

U=$\frac{x^3}{3}-\frac{5x^2}{2}+6x+3$

$\frac{dU}{dx}=x^2-5x+6=0$

x=2,3

potential energy is minimum when x=3

at x=3 potential energy =7.5

kinetic energy =total energy-potential energy$=17-7.5=9.5J$