1. What is the Formula's for Kinetic and Potential Energy?

Let f(x) = x4- 8x2 . find the relativeextrema of this function using the second derivative test.

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 710 n/m. it is initially at rest on an inclined plane that is at an angle of θ = 23° with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is μk = 0.19. in the initial position, where the spring is compressed by a distance of d = 0.16 m, the mass is at its lowest position and the spring is compressed the maximum amount. take the initial gravitational energy of the block as zero. a) what is the block's initial mechanical energy? b) if the spring pushes the block up the incline, what distance, l, in meters will the block travel before coming to rest? the spring remains attached to both the block and the fixed wall throughout its motion.

For this car, predict the shape of a graph that shows distance (x) versus time (t). note that time is the independent variable and will be on the bottom axis. need asap