Physics for Dentistry and Medicine students PHYS 145

Text book

Physics

; John D. Cutnell and Kenneth W. Johnson; 7 th edition; Wiley; 2007.

Chapter 2

Kinematics in One Dimension As this barn owl comes in for a landing, it is slowing down while moving forward. To describe such motion, this chapter presents the concepts of displacement, velocity, and acceleration. (Manfred Danegger/Photo Researchers, Inc.)

Displacement and Distance

• •

Definition:

The displacement is a

vector

that points from an object’s initial position to its final position and has a magnitude that equals the shortest distance between the two positions.

SI Unit of Displacement: meter (m)

Speed and Velocity

•

Average Speed

Average speed

 Distance

Elapsed time

• •

Definition of Average Velocity

Average v velocity

  

x t

 

t x



o o

 Displaceme 

Elapsed



x

 

t

nt

time

SI Unit of Average Velocity and Speed: meter per second (m/s)

Instantaneous Velocity

• The

instantaneous velocity v

of the car indicates how fast the car moves and the direction of the motion at each instant of time. The magnitude of the instantaneous velocity is called the

instantaneous speed,

and it is the number (with units) indicated by the speedometer

v

  lim 

t

 0   

x t

•

Acceleration

Definition of Average Acceleration

Average accelerati on



Change in velocity



a

 

v t

 

v o



t o

 

Elapsed



v



t time SI

Unit of Average Acceleration:

(m/s 2 )

• The

instantaneous acceleration



a

 lim 

t

 0 

v

 

t

Equations of Kinematics for Constant Acceleration

Equation

v = v o x = ½ (v o + at +v) t x = v o t + ½ at 2 v 2 = v o 2 + 2ax x a

Variable

v v o t -

Freely Falling Bodies

• In the absence of air resistance , it is found that all bodies at the same location above the earth fall vertically with the same acceleration .

• The acceleration of a freely falling body is called the

acceleration due to gravity

g g = 9.80 m/s 2 or 32.2 ft/s 2 Demo

(a) In the presence of air resistance, the acceleration of the rock is greater than that of the paper.

(b) In the absence of air resistance, both the rock and the paper have the same acceleration.

Example

• A stone is dropped from rest from the top of a tall building, as the figure indicates. After 3.00 s of free fall , what is the displacement

y

of the stone?

Graphical Analysis of Velocity and Acceleration

• A graph of position

vs

. time for an object moving with a constant velocity of

v

= Slope

= Δx/

Δ

t =

+8

m/

+2

s = +4 m/s.

Example 16:

A Bicycle Trip

A velocity

vs

. time graph that applies to an object with an acceleration of

a

= Slope

= Δv/

Δ

t =

+12

m.s

-1 /

+2

s = +6 m/s 2 .

The initial velocity is

v o = +5 m/s

when

t = 0 s.

Problems

1/203)

A whale swims due east for a distance of 6.9 km, turns around and goes due west for 1.8 km, and finally turns around again and heads 3.7 km due east. (a) What is the total distance traveled by the whale? (b) What are the magnitude and direction of the displacement of the whale?

Solution: a) b) 12.4 km.

8.8 km due east.

Problems

2/203) You step onto a hot beach with your bare feet. A nerve impulse, generated in your foot, travels through your nervous system at an average speed of 110 m/s . How much time does it take for the impulse, which travels a distance of 1.8 m , to reach your brain?

Solution: x = ½ (v o +v) t 1.8 m = 110 m/s t t = 0.016 s

Solve This Problem 19/205)

In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints to a speed of 6.0 m/s in 1.5 s. Assuming that the player accelerates uniformly, determine the distance he runs .

Problems

• 32/206) The left ventricle of the heart accelerates blood from rest to a velocity of +26 cm/s . (a) If the displacement of the blood during the acceleration is +2.0 cm , determine its acceleration (in cm/s 2 ). (b) How much time does blood take to reach its final velocity?

Solution: a) v 2 = v o 2 (26) 2 + 2ax = 0 + 2 (a) 2.0 cm a = 169 cm/s 2 b) v = v o + at 26 = 0 + 169 t t = 0.15 s

Problems

37/208)

The greatest height reported for a jump into an airbag is 99.4 m by stuntman Dan Koko. In 1948 he jumped from rest from the top of the Vegas World Hotel and Casino. He struck the airbag at a speed of 39 m/s. To assess the effects of air resistance, determine how fast he would have been traveling on impact had air resistance been absent.

Solution: a) v 2 = v o 2 (v) 2 + 2ax = 0 + 2 (-9.8) (- 99.4 m) v = 44.13 m/s

H.W.

• 41/210) A wrecking ball is hanging at rest from a crane when suddenly the cable breaks. The time it takes for the ball to fall halfway to the ground is 1.2 s. Find the time it takes for the ball to fall from rest all the way to the ground.

Problems

57/211)

A snowmobile moves according to the velocity –time graph shown in the drawing. What is the snowmobile’s average acceleration during each of the segments

A, B, and C?

Problems

58/212)

A person who walks for exercise produces the position–time graph given with this problem. (a) Without doing any calculations, decide which segments of the graph (

A, B, C, or D)

indicate

+ve, -ve,

and zero average velocities

.

(b) Calculate the average velocity for each segment to verify your answers to part (a).