honors physics : lecture 1, pg 1 honors physics “mechanics for physicists and engineers” agenda...

Honors Physics : Lecture 1, Pg 1

Honors Physics Honors Physics “Mechanics for Physicists and Engineers”“Mechanics for Physicists and Engineers”

Agenda for TodayAgenda for Today

AdviceAdvice 1-D Kinematics1-D Kinematics

Average & instantaneous velocity and accelerationMotion with constant accelerationFreefall


Kinematics ObjectivesKinematics Objectives

Define average and instantaneous velocity Caluclate kinematic quantities using equations interpret and plot position -time graphs be able to determine and describe the meaning of the

slope of a position-time graph


KinematicsKinematics

Location and motion of objects is described using Kinematic Variables:

Some examples of kinematic variables.position rr vector, (d,x,y,z)velocity vv vectoracceleration a vector

Kinematic VariablesKinematic Variables: : Measured with respect to a reference frame. (x-y axis)Measured using coordinates (having units).Many kinematic variables are VectorsVectors, which means they

have a directiondirection as well as a magnitudemagnitude.Vectors denoted by boldface VV or arrow above the variable


MotionMotion

Position: Separation between an object and a reference point (Just a point)

Distance: Separation between two objects Displacement of an object is the distance between it’s

final position df and it’s initial position d i (d f - di)= d Scalar: Quantity that can be described by a

magnitude(strength) onlyDistance, temperature, pressure etc..

Vector: A quantity that can be described by both a magnitude and direction Force, displacement, torque etc.


Speed describes the rate at which an object moves. Distance traveled per unit of time.

Velocity describes an objects’ speed and direction. Approximate units of speed

40 km/hr 25 miles/hr 11 m/s



Speed and VelocitySpeed and Velocity


Motion in 1 dimensionMotion in 1 dimension In general, position at time t1 is usually denoted d, rr(t1) or x(t1)

In 1-D, we usually write position as x(t1 ) 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 = t2 - t1 is x = x2 - x1= d2 -d1

t

x

t1 t2

x

t

x1

x2some particle’s trajectory

in 1-D


1-D kinematics1-D kinematics

t

d

ttvav

12

) d1- (d2

t

x

t1 t2

x

d1

d2trajectory

Velocity v is the “rate of change of position” Average velocity vav in the time t = t2 - t1 is:

t

Vav = slope of line connecting x1 and x2.


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...1-D kinematics...

dt

tdxtv

)()(

t

x

t1 t2

x

x1

x2

t

so V(t2 ) = slope of line tangent to path at t2.

t

d

ttvav

12

) d1- (d2

»Calculus Notation


More 1-D kinematicsMore 1-D kinematics

We saw that v = x / t so therefore x = v t ( i.e. 60 mi/hr x 2 hr = 120 mi )See text: 3.2

In “calculus” language we would write dx = v dt, which we can integrate to obtain:

x t x t v t dtt

t( ) ( ) ( )2 1

1

2

Graphically, this is adding up lots of small rectangles:

v(t)

t

+ +...+

= displacement

v

t1 2

60


1-D kinematics...1-D kinematics...

av t v t

t t

v

tav

( ) ( )2 1

2 1

Acceleration a is the “rate of change of velocity” Average acceleration aav in the time t = t2 - t1 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.

a tdv t

dt

d x t

dt( )

( ) ( ) 2

2


Problem SolvingProblem Solving

Read !Before 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.

Watch your units !Always check the units of your answer, and carry the units

along with your numbers during the calculation.

Understand the limits !Many 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).


IV. Displacement during acceleration.IV. Displacement during acceleration.

You accelerate from 0 m/s to 30 m/s in 3 seconds, how far did you travel?

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? df=1/2at2 + vit + di

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? d = (vf2 - vi2) /2a


RecapRecap

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 x t ( )

x

a

vt

t

ta

v t v t

t t

v

tav

( ) ( )2 1

2 1

vx t x t

t t

x

tav

( ) ( )2 1

2 1


RecapRecap So for constant acceleration we find:

v v at 0

x x v t at 0 021

2

a const

x

a

v t

t

tv v a x x

v v vav

22

12

2 1

1 2

2

1

2

( )

( )

From which we can derive:


IV. Acceleration due to gravityIV. Acceleration due to gravity

The acceleration of a freely falling object is 9.8 m/s2 (32 ft/s2) towards the earth.

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).

Neglecting air resistance, an object has the same acceleration on the way up as it does on the way down.

Use the same equations of motion but substitute the value of ‘g’ for acceleration ‘a’.


Recap of kinematics lecturesRecap of kinematics lectures Measurement and Units Measurement and Units (Chapter 1)(Chapter 1)

Systems of unitsConverting between systems of unitsDimensional Analysis

1-D Kinematics 1-D Kinematics Average & instantaneous velocity

and and accelerationMotion with constant acceleration

honors physics : lecture 1, pg 1 honors physics “mechanics for physicists and engineers” agenda...

Documents