Lecture 3. (sections )

Transcription

1 Lecture 3 PHYSICS 201 (sections ) Instructor: Hans Schuessler Temporary: Alexandre e Kolomenski o

2 Average velocity v Δx Δt

3 Instantaneous velocity v Δx lim when Δt 0 Δt

4 Average Velocity (example) x (meters) t (seconds) What is the average velocity over the first 4 seconds? A) -2 m/s B) 4 m/s C) 1 m/s D) not enough information to decide.

5 Instantaneous Velocity x (meters) t (seconds) What is the instantaneous velocity at the fourth second? A) 4 m/s B) 0 m/s C) 1 m/s D) not enough information to decide.

6 Acceleration We say that things which have changing velocity are accelerating Acceleration is the Rate of change of velocity You hit the accelerator (what about break?) in your car to speed up (Ok It s true you also hit it to stay at constant velocity, but that s because friction is slowing you down we ll get to that later )

7 Average acceleration a Δv Δt Unit of acceleration: (m/s)/s=m/s 2 Meters per second squared

8 Acceleration

9 KINEMATICS IN ONE DIMENSION Equations of Kinematics for Constant Acceleration A position of an object is a function of time x x(t) Average velocity v Average acceleration x t t a x 0 0 v t We can always select the reference frame in such a way that, v t 0 0 t 0 and x x ( t 0) 0, then Average acceleration v x t

10 Kinematics atcs in one dimension so (cont.) Motion with constant acceleration. From the formula Average acceleration v v t a 0 We find v v 0 at On the other hand Average velocity v x t 1 1 v ( v0 v) ( v0 ( v0 at)) v at 2 Then we can find x v t x ( v 0 at ) t x 0 v 0t at How to directly relate x, v and a?

11 Units SI Displacement, distance: 1 meter 1m Velocity, speed: 1 meter/second 1m/s (speed is the magnitude of velocity-scalar!) Acceleration: 1 meter/second 2 1m/s 2

12 Velocity for motion with positive acceleration

13 Velocity for motion with negative acceleration

14 Graphing motion with velocity constant on time intervals

15 Position, Velocity and Acceleration Displacement, Velocity and Acceleration are all related If velocity is constant, then the acceleration is 0 and the displacement is changing linearly with time. If acceleration is constant, then the velocity is changing linearly and the displacement is a quadratic function of time (parabola or parabolic dependence).

16 Qualitative graphical analysis x v t For x(t) the slope is increasing then decreasing (this slope is proportional to velocity, Therefore we can draw approximate graph hfor the velocity ) a t t For v(t) the slope is related to acceleration. (we can see that the acceleration is positive, then goes through zero, and then becomes negative).

17 Example of graphic solution: Catching a speeder Speeder - with constant velocity Police car - with acceleration

18 Examples Can a car have uniform speed and non-constant velocity? Can an object have a positive average velocity over the last hour, and a negative instantaneous velocity?

19 Conceptual Example If the velocity of an object is zero, does it mean that the acceleration is zero? If the acceleration is zero, does that t mean that t the velocity is zero?

20 Galileo Galilei A paradox is a friend of a genius WHO WAS GALILEO? Galileo was an Italian physicist and astronomer credited with building the first effective telescope. He used this to prove that the earth moves round the sun. This confirmed the theory originally put forward by the Polish astronomer Nicholas Copernicus. But it went directly against the teachings of the Church i.e; the earth was the centre of the Universe and the Sun revolved round the Earth. It was this conflict with the teachings of the Church that was to eventually bring Galileo to the attention of the Inquisition Experiments on the motion of objects falling under the action of the force of gravity LEANING TOWER of PISA Galileo Galilei ( ) Years Built: Height: meters (185 feet). 8 stories. Lean: 5.2 meters (1997)

21 Testing Kinematics for a=9.80m/s 2

22 Objects in the field of gravity. All objects fall with the same constant acceleration, when air resistance is negligible!!!

23 1-D motions in the gravitational field

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27 Thanks for your attention!