2. Honors Physics : Lecture 1, Pg 1 Honors Physics “Mechanics for Physicists and Engineers” Agenda for Today l Advice l 1-D Kinematics çAverage & instantaneous velocity and acceleration çMotion with constant acceleration çFreefall

3. Honors Physics : Lecture 1, Pg 2 Kinematics Objectives l Define average and instantaneous velocity l Caluclate kinematic quantities using equations l interpret and plot position -time graphs l be able to determine and describe the meaning of the slope of a position-time graph

4. Honors Physics : Lecture 1, Pg 3 Kinematics l Location and motion of objects is described using Kinematic Variables: l Some examples of kinematic variables. r çposition rvector, (d,x,y,z) v çvelocity vvector çacceleration a vector l Kinematic Variables: çMeasured with respect to a reference frame. (x-y axis) çMeasured using coordinates (having units). Vectors directionmagnitude çMany kinematic variables are Vectors, which means they have a direction as well as a magnitude. V çVectors denoted by boldface V or arrow above the variable

5. Honors Physics : Lecture 1, Pg 4 Motion Motion l Position: Separation between an object and a reference point (Just a point) l Distance: Separation between two objects l Displacement of an object is the distance between it’s final position d f and it’s initial position d i (d f - d i )=  d l Scalar: Quantity that can be described by a magnitude(strength) only çDistance, temperature, pressure etc.. l Vector: A quantity that can be described by both a magnitude and direction ç Force, displacement, torque etc.

6. Honors Physics : Lecture 1, Pg 5 l Speed describes the rate at which an object moves. Distance traveled per unit of time. l Velocity describes an objects’ speed and direction. l Approximate units of speed Speed and Velocity

7. Honors Physics : Lecture 1, Pg 6 Motion in 1 dimension r l In general, position at time t 1 is usually denoted d, r(t 1 ) or x(t 1 ) l In 1-D, we usually write position as x(t 1 ) but for this level we’ll use d Since it’s in 1-D, all we need to indicate direction is + or . Displacement in a time  t = t 2 - t 1 is  x = x 2 - x 1 = d 2 -d 1 t x t1t1 t2t2  x  t x1x1 x2x2 some particle’s trajectory in 1-D

8. Honors Physics : Lecture 1, Pg 7 1-D kinematics t x t1t1 t2t2  x d1d1 d2d2 trajectory l Velocity v is the “rate of change of position” Average velocity v av in the time  t = t 2 - t 1 is:  t V av = slope of line connecting x 1 and x 2.

9. Honors Physics : Lecture 1, Pg 8 Instantaneous velocity v is defined as the velocity at an instant of time (  t= 0) Slope formula becomes undefined at  t = 0 1-D kinematics... t x t1t1 t2t2  x x1x1 x2x2  t so V(t 2 ) = slope of line tangent to path at t 2. »Calculus Notation

10. Honors Physics : Lecture 1, Pg 9 More 1-D kinematics We saw that v =  x /  t  so therefore  x = v  t ( i.e. 60 mi/hr x 2 hr = 120 mi ) çSee text: 3.2 l In “calculus” language we would write dx = v dt, which we can integrate to obtain: l Graphically, this is adding up lots of small rectangles: v(t) t ++...+ = displacement v t 12 60

11. Honors Physics : Lecture 1, Pg 10 1-D kinematics... l Acceleration a is the “rate of change of velocity” Average acceleration a av in the time  t = t 2 - t 1 is: And instantaneous acceleration a is defined as:The acceleration when  t = 0. Same problem as instantaneous velocity. Slope equals line tangent to path of velocity vs time graph.

12. Honors Physics : Lecture 1, Pg 11 Problem Solving l Read ! çBefore you start work on a problem, read the problem statement thoroughly. Make sure you understand what information in given, what is asked for, and the meaning of all the terms used in stating the problem. l Watch your units ! çAlways check the units of your answer, and carry the units along with your numbers during the calculation. l Understand the limits ! çMany equations we use are special cases of more general laws. Understanding how they are derived will help you recognize their limitations (for example, constant acceleration).

13. Honors Physics : Lecture 1, Pg 12 IV. Displacement during acceleration. l You accelerate from 0 m/s to 30 m/s in 3 seconds, how far did you travel? l What if a car initially at 10 m/s, accelerates at a rate of 5 m/s2 for 7 seconds. How far does it move? ç df=1/2at2 + vit + di l C. An airplane must reach a speed of 71 m/s for a successful takeoff. What must be the rate of acceleration if the runway is 1.0 km long? ç d = (vf2 - vi2) /2a

14. Honors Physics : Lecture 1, Pg 13 Recap l If the position x is known as a function of time, then we can find both velocity v and acceleration a as a function of time! x a v t t t

15. Honors Physics : Lecture 1, Pg 14 Recap l So for constant acceleration we find: x a v t t t l From which we can derive:

16. Honors Physics : Lecture 1, Pg 15 IV. Acceleration due to gravity l The acceleration of a freely falling object is 9.8 m/s2 (32 ft/s2) towards the earth. l The farther away from the earth’s center, the smaller the value of the acceleration due to gravity. For activities near the surface of the earth (within 5-6 km or more) we will assume g=9.8 m/s2 (10 m/s2). l Neglecting air resistance, an object has the same acceleration on the way up as it does on the way down. l Use the same equations of motion but substitute the value of ‘g’ for acceleration ‘a’.

17. Honors Physics : Lecture 1, Pg 16 Recap of kinematics lectures l Measurement and Units (Chapter 1) çSystems of units çConverting between systems of units çDimensional Analysis l 1-D Kinematics çAverage & instantaneous velocity and and acceleration çMotion with constant acceleration

18. Honors Physics : Lecture 1, Pg 17