Lecture 5 Introduction to Physics PHY101 Chapter 2 Equations of Kinematics for Constant Acceleration in 1 Dim 2 4 2 5 2 7 Free Fall 2 6 Chapter 3 Equations of Kinematics for Constant Acceleration in 2 Dim 3 1 3 2 Physics 101 Lecture 6 Pg 1 Summary of concepts from last lecture position your coordinates just x in 1 D displacement x change of position velocity rate of change of position average x t instantaneous slope of x vs t lim t 0 x t acceleration rate of change of velocity average v t instantaneous slope of v vs t lim t 0 v t Physics 101 Lecture 6 Pg 2 Concept Question A car is moving along the negative x direction During part of the trip the speed increases from 16 to 28 m s in 1 5 s Which of the following is correct v 1 v 0 a 0 x a 2 v 0 a 0 3 v 0 a 0 correct 4 v 0 a 0 another part of the trip the speed decreases from During 48 to 26 m s in 11 s Which of the following is correct 1 2 3 4 v 0 v 0 v 0 v 0 a 0 a 0 a 0 correct a 0 v a x If speed is increasing v and a are in same direction If speed is decreasing v and a are in opposite direction Physics 101 Lecture 6 Pg 3 Concept Question Which of the following statements is most nearly correct 1 A car travels around a circular track with constant velocity 2 A car travels around a circular track with constant speed 3 Both statements are equally correct correct On a circular track the direction that the car is traveling in is always changing and since velocity takes into account the direction of travel the velocity is always changing Speed however is independent of direction and so the speed can stay constant Physics 101 Lecture 6 Pg 4 Kinematics in One Dimension Constant Acceleration Consider an object which moves from the initial position x 0 at time t0 with velocity v0 with constant acceleration along a straight line How does displacement and velocity of this object change with time aav a v v0 t t0 v t v0 a t t0 1 vav x x0 t t0 v v0 2 x x0 t t0 v v0 2 2 Use Eq 1 to replace v in Eq 2 x t x0 t t0 v0 a 2 t t0 2 3 Use Eq 1 to replace t t0 in Eq 2 v2 v02 2 a x x0 4 Physics 101 Lecture 6 Pg 5 Application of Eqs of Kinematics A runner accelerates to a velocity of 5 36 m s due west in 3 00 s His average velocity is 0 640 m s 2 due west What was his velocity when he began accelerating Chapter 2 problem 15 t0 0 s v 5 36 m s t 3 00 s aav 0 640 m s2 v0 m s aav v v0 t t0 v0 v aav t t0 3 44 m s v0 3 44 m s due west Physics 101 Lecture 6 Pg 6 Application of Eqs of Kinematics A drag racer starting from rest speeds up for 402 m with a 17 m s2 A parachute then opens slowing the car down with a 6 10 m s2 How fast is the racer after moving 3 50 x 102 m after the parachute opens 2 28 1 Before the parachute opens car moves x direction t0 0 s v01 0 m s x1 402 m a1 17 m s2 2 After the parachute opens t0 0 s x2 3 50 x 102 m a2 6 10 m s2 v m s v2 v022 2 a2 x2 Get v022 from 1 v02 2 a1 x1 1 2 117 m s v2 v02 2 a 2 x2 1 2 96 9 m s Physics 101 Lecture 6 Pg 7 Free Fall Free fall is the idealized description of the motion of a downward falling body due to gravity Air resistance is neglected Acceleration due to gravity is considered to be constant The acceleration due to gravity is always pointing downward with magnitude g 9 80 m s2 Physics 101 Lecture 6 Pg 8 Concept Question An object is dropped from rest If it falls a distance D in time t then how far will it fall in a time 2t 1 2 3 4 5 D 4 D 2 D 2D 4D Correct x 1 2at2 Followup question If the object has speed v at time t then what is the speed at time 2t 1 2 3 4 5 v 4 v 2 v 2v 4v Correct v at Physics 101 Lecture 6 Pg 9 Concept Question A ball is thrown vertically upward At the very top of its trajectory which of the following statements is true 1 velocity is zero and acceleration is zero 2 velocity is not zero and acceleration is zero 3 velocity is zero and acceleration is not zero 4 velocity is not zero and acceleration is not zero correct The velocity vector changes from moment to moment buts its acceleration vector does not change Though the velocity at the top is zero the acceleration is still constant because the velocity is changing Physics 101 Lecture 6 Pg 10 Free Fall A wrecking ball is hanging from rest from a crane when suddenly the cable breaks The time it takes the ball to fly half way to the ground is 1 2 s Find the time for the ball to fall from rest all the way to the ground 2 45 1 Half way to the ground y direction t0 0 s v0 0 m s t 1 2 s a 9 80 m s2 Y1 2 v0 t a t2 7 1 m 2 From rest all the way to the ground y 2 Y 1 2 t0 0 s v0 0 m s a 9 80 m s2 t s Y v0 t a t2 a t2 t 2 y a 1 2 1 7 s Physics 101 Lecture 6 Pg 11 Concept Question Dennis and Carmen are standing on the edge of a cliff Dennis throws a basketball vertically upward and at the same time Carmen throws a basketball vertically downward with the same initial speed You are standing below the cliff observing this strange behavior Whose ball is moving fastest when it hits the ground 1 Dennis ball 2 Carmen s ball 3 Same Correct v2 v02 2g y Carmen v0 v0 Dennis H vA vB Physics 101 Lecture 6 Pg 12 Kinematics in Two Dimensions Constant Acceleration Consider an object which moves in the x y plane from the initial position r0 at time t0 with velocity v0 with constant acceleration position your coordinates just r x y in 2 D displacement r r r0 change of position velocity rate of change of position average r t instantaneous lim t 0 r t acceleration rate of change of velocity average v t …