Show that if the net force on a particle constrained to move in 1 dimension depends only on position, f-f), the newton's second law can be solved to find v as a function ofx given by: 1 dv2 2 dx v2-si +副0f(x')dx'. note: use the chain rule: dt- = 2dte b) consider a mass constrained to move along x-axis and subject to a net force f =-kx, where k > 0 is a constant. the mass is released form rest at x xo at t-0. use the equation for velocity from part a) to find (x) = . separate the variables and integrate to obtain the time dependence of the position of this mass. hint: when solving the awkward integral you will obtain, use first the suband then ucos 0 in subsequent integral. dt dx dt dx

Ablock of mass m = 2.5 kg is attached to a spring with spring constant k = 790 n/m. it is initially at rest on an inclined plane that is at an angle of 28 degrees with respect to the horizontal, and the coefficient of kinetic friction between the block and the plane is k = 0.14. in the initial position, where the spring is compressed by a distance of a = 0.18 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. 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.

What is friction? how does it affect the motion of an object?

If the area of a square has increased by a factor of 16, by how much has each side increased?