Please solve this tasks and explain with all details the solution, because I am preparing for the exam and there is a chance that I will have similiar tasks. Thank you in advance

Quiz 3 - Energy and Work Unless specified otherwise, assume g = 9.81 m/s. Problem 1 (25 pts) - Energy A father running after his daughter has half the kinetic energy of the daughter, who has half the mass of the father. The father speeds up by 1 m/'s and then has the same kinetic energy as the daughter. What are the original speeds of (a) the father and (b) the daughter? Problem 2 (25 pts) - Force and Work A 3-kg body is at rest on a frictionless surface when a constant horizontal force F acting in the positive direction of an x axis along the track is applied to the body at t = 0 s. A graph of the position of the object is shown below. How much work is done on the body by the applied force F between t = 0 and t = 2 s? 1= 0 t= Is t=1.5s t=2s 0.2 0.4 0.6 0.8 t = 0.5 s x (m) Problem 3 (25 pts) - Potential Energy The spring of k = 10 N/m is compressed by 5.5 cm and used to propel a 3.8 g cork from the gun. What is the speed of the cork if it is released as the spring passes through its relaxed position? Assume zero energy losses.Problem 4 {25 Hts! Work Done [II External Forces An object is sliding on a horizontal surface, attached to one end ofa spring with stiffness coefcient of it = 4 Him. The object has a kinetic energyr oiKD= 2t] .l as it passes through the spring's equilibrium position. As the object slides. a constant Frictional force of magnitude It'll-l N acts on it. Answer the following: {a} How far [or] will the object slide to the right from the equilibrium position before coming momentarily.r to rest? {l5 [its] {b} What will be the kinetic energy of the object as it slides back through the equilibrium position? [It] pts}