Question

answer it please....

Answer 1

Okay, by law of conservation of mechanical energy, kinetic energy (hence the speed) will be max when potential energy is minimum.

Now we differentiate x^2\2 -x with respect to x

that gives x-1

x=1 is a turning point in U vs x graph

we can double differentiate , we get 1, which is positive. Hence we get a minimum at x=1.

at x=1 U= -1/2

U+K = constant =2

K=2.5 J

1/2 m v^2 = 2.5 J

v^2=5

v= sqrt (5)

Hope this helps.

I assumed you know enough calculus to find minima and maxima of functions.