Physics 534 Chapter 9

8/8/2019 Physics 534 Chapter 9

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Chapter 9



Uniform Motion

The simplest motion is straight line motion in a specific direction at a constant speed.

When both speed and direction remain thesame, it is called uniform motion.

Speed is a scalar quantity, = distance/time.

Velocity is the vector quantity denoting speed and direction.

Velocity is the displacement of an objectper unit of time.

V = d/t, d - displacement, t ± time

interval.



Random Motion

The motion of these particles are random

because their speed and direction change.

This is an example of the KineticMolecular Theory (Chemistry).



Graphing Distance-Time

Time is independent and on the x-axis.

Distance depends on time and is on the y-

axis. The slope of the graph gives us the speed.

If it was a displacement-time graph, slope

would give the velocity.



Graphing Displacement

Velocity is considered to be dependent on

time.

Average velocity = total displacementtotal time

av = d/t



Calculating Speed

Average speed = total distance

total time

av = dtotal/t



Activity

Page 194, Q. 1-3

Page 196, Q. 1-3

Investigation, Page 196 Lab: Uniform Motion



Activity

Page 199, Q. 1,4



Velocity at a Point

This is done by taking the slope of a line

that touches at the specific time.

See page 207 for examples.



Activity

Page 203, Q. 1-4

Page 208, Q. 1-4



Average Velocity

Average Velocity is defined as the change

in displacement over time.

av = d/ t Average Speed is the change in distance

over time.

av = d/ t or under uniform acceleration = v2 + v1

2



Pr o jectile Motion

Pr o jectile Motion



Distance f r om Speed

We already know that speed = distance

time

So distance = speed x time Distance can be determined by the area

under the curve of a velocity-time graph.



Acceleration

Acceleration is the change in velocity with time.

Acceleration = change in velocity

time interval

a = v = v2 ± v1

t t

a is the acceleration, m/s/s = m/s2

v2 is the final velocity, m/s v1 is the initial velocity, m/s

A negative acceleration = a deceleration



Getting Info f r om a Graph

Fr om a graph of velocity-time, the distance

is the area under the graph.

Fr om a graph of velocity-time, theacceleration is f r om the slope.

Fr om a graph of acceleration-time, the

velocity is the area under the graph.

Page 213, Q. 1



Activity

A car accelerates f r om 0 to 100 km/h in 10s.

What is the acceleration, in m/s2?

a = v = v2 ± v1 = 100 km/h ± 0 km/h

t t 10s

= 10 km/h/s

10 km x 1 hr x 1000m = 2.78 m/s2

hr 3600s km

Do page 215, Q. 1-3, page 217, Q. 1,2



Final Velocity

Velocity can be calculated if we consider it

in terms of the initial velocity which has

under gone acceleration or deceleration.

v = u + at

v = final velocity, in m/s

u = initial velocity, in m/s a = acceleration, in m/s2

t = time of acceleration, in seconds



Activity

What is the final velocity of a person

walking at 4 m/s who accelerates at 1 m/s2

for 5 s?

v = u + at

= 4m/s + 1m/s2 x 5s

= 4m/s + 5m/s = 9m/s



Distance Covered

Distance can be determined if the initial

velocity, time and acceleration are known.

s = ut + ½ at2

s = distance, m

u = initial velocity, m/s

t = time, seconds a = acceleration m/s2



Activity

What is the depth of a well, if when you

dr op a r ock, it takes 5 seconds to hit the

bottom?

s = ut + ½ at2

= 0(5) + ½ (9.81m/s2)(5s)2

= 0 + ½ (9.81)(25) = 122.625 m



Hor izontal vs Vertical Motion

ONLY in situations where objects aremoving vertically thr ough space, theacceleration is 9.81 m/s2.

An object dr opped has an initial velocity of 0 m/s.

The acceleration due to gravity slows

objects moving upwards and speeds upobjects moving downwards.

Do page 221, Q. 1-4, p. 225, Q. 1-4



Short Cut

What is the final velocity of a car if it starts

at 10 m/s and accelerates at 2 m/s2 over a

distance of 100m?

v2 = u2 + 2as

= (10 m/s)2 + 2(2m/s2)(100m)

= 100 + 400 v2 = 500

v = 22.4 m/s



Exam Question

A motorcyclist, travelling at a speed of 30 m/s, sees an obstacle 100 metres in front of him and

puts on the brakes. He hits it 5.0 seconds later.

If the motorcycle slows down uniformly, how fast was it going at the instant of the collision?

A) 10.0 m/s

B) 8.0 m/s

C) 6.0 m/s

D) 4.0 m/s



Exam Question

From t top of a tower an object i t rown verticall downward wit a velocit of 20 m/

What i the velocit of the object af ter it has fallen 60 metres?

A) 55 m/s

B) 50 m/s

C) 45 m/s

D) 40 m/s



Summary

When air resistance is negligible, all f reelyf alling objects have the same downwardacceleration.

A ball r olling down an incline has uniformacceleration.

Acceleration due to gravity has a value of

9.81 m/s2

. Equations der ived for uniform acceleration

apply to f reely f alling objects.



Summary

A negative slope on a straight line position-time graph indicates motion in a negative

direction at constant velocity.

Average velocity = displacement/time intervalwhich can be taken at any 2 times on a

position-time graph.

Average speed = total distance/time interval Instantaneous velocity can be taken f r om the

slope of the tangent to the curve at that time.



Summary

Velocity is a vector quantity which may befound if the velocity is uniform, withvelocity = displacement/time.

Speed is a scalar quantity which may befound, if the speed is uniform, withspeed = distance/time.

The position-time graph for an objectmoving with uniform motion is a straightline. The slope of the straight line givesthe velocity.



Summary

Acceleration is the rate of change of

velocity over time.

a = /t = (2- 1)/t On velocity-time graphs, a straight line

shows that an object has a constant

acceleration.

On a velocity-time graph, the acceleration

is the slope of the line.



Summary

A negative slope on a velocity-time graphmeans that the magnitude of the velocity is

decreasing, if the object is moving in a

positive direction.

The area under the velocity-time graph

gives the displacement.

v = u + at

s = ut + ½ at2

v2= u2 + 2as



Summary

If the motion is in a straight line, the vector

notation may be omitted and +/- signs

used instead.

A curved velocity-time graph indicates a

changing acceleration. The average

acceleration for an interval is found by

finding the slope between two points on the graph.



Summary

The acceleration at any point on a curved

velocity-time graph is the slope of the tangent to

the curve at that point.

To construct a velocity-time graph f r om a ticker tape recording, mark the tape into lengths of the

same time interval. The displacement for each

interval divided by the time gives the average

velocity for that interval. Plotting the averagevelocity for each interval versus the time will

yield a velocity-time graph.



Exam Question

A diver jumps from a height of 3.0 metres above the height of the water and touches the surface

1.0 s later.

What was his velocity when he hit the water?

A) 8.0 m/s

B) 7.0 m/sC) 6.0 m/s

D) 5.0 m/s



Activity

Page 242, Q. 16-19, 22, 23,

27, 40, 46, 50, 51, 56, 58

Physics 534 Chapter 9

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