science 10 physics summaries

8/3/2019 science 10 physics summaries

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Unit 3: Motion

Chapter 8: Average velocity is the rate of change in position

8.1 The Language of Motion

y Magnitude describes the size of a measurement

y The symbol for change= which means delta- Greek letter

y Vector:

- Vector quantities include magnitude and direction

- Vector abbreviations are written in bolded italics with an arrow above

them, such as vfor velocity and dfor position.

- When a direction is written in a vector description, it is usually

abbreviated and put into square brackets, such as 12km [W] for 12 km

west

y Scalar:

- Scalar quantities include magnitude only.

- Scalars are not written with any abbreviations or italics

Measurement Explanation Classification

Distance (d)

(m)

(km)

Shows the extent of a course

between two points

Scalar

Position (d)

(m)

(km)

Shows the location of an

object relative to the point of

origin (where the object first

started off from)

Vector

(includes direction)

Vectors Scalars

Magnitude Magnitude

Direction

Vectors and Scalars


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Time (t)

Seconds (s)

Hours (h)

Describes when an event takes

place

Scalar

Time interval( t)

The difference between initial

time (when an even starts) and

final time (when an event

ends)

*The duration of an event

Scalar

To calculate:

t= tf(final time) ti

(initial time)

Displacement

( d)

(m) (km)

Describes how much an

objects position has changed

in a straight line from the

point of origin.

*if an object ends up back towhere it started from then you

could say that the objects

displacement is zero.

Vector

To calculate:

d= df(final position )

di (initial position)

y It is important to know the different between displacement and distance

- An ant travels 2cm north, 6cm west, 2cm south, and 2cm east.

The ants distance:

2cm+6cm+4cm+2cm= 14cm

The ants displacement:

d= 4cm

The ants displacement is 4cm because it has moved 4cm

from its initial position. It the ant had returned back to its

initial position, then its displacement would be 0m.

Displacement vs. Distance


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y Distance:

W E

A car travelled 7km east to the mall from the gas station. The total distance

travelled from the gas station to the mall is 7 km.

y Position:

If the car traveled 7 km to the mall, what is the cars position? The direction or

position of the car from the gas station is 7 km [E]. If the car was to return back to

the gas station, its position would be 0 km since the car is back to the origin.

y Time interval:

t=0s t=3s t=8s

W E

Suppose a person walking on a sidewalk is walking at 1m/s [E]. She walks from her

house at 0m. She passed the stop sign at 3m [E] and then passed the lamp post at

8m [E]. How long did it take her to walk that distance from the stop sign to the

lamp post?

3m [E] =3s (initial time) 8s 3s = 5s

8m [E] =8s (final time)

Examples


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y Displacement

It took her 5s to walk from the stop sign to the lamp post. Her position at 8s is 8m

[E], and at 3s its 3m [E].

In the time interval of 3s-8s her displacement is

3s=3m [E]

8s=8m [E]

8m [E] 3m [E]

= 5m [E]

Between t=3s and t=5s, the displacement of the girl is 5m [E]. This Vector quantity

represents how much the girls position changed between the time intervals of 3s-

8s. Her displacement from the point of origin (her house) to the lampost is 8m [E].

if she goes back to her house, her displacement would go back to 0m.

y

To indicate opposite directions in vector quantities, opposite signs are used.Here are some common signs that are used in physics to show direction:

North Up +

West East

Left Right

- +

* If an object passes the point of origin, the

direction changes.

South Down -

Direction and Si ns


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y All objects in uniform motion meet the following conditions:

- Travel in equal displacements in equal time intervals

- Objects do not speed up, slow down, or change direction

y

Motion of an object can me analyzed in many ways:- Motion diagram: shows us the objects position at given times and allows

us to visualize the objects motion.

-Position- Time graph: plots position data on the vertical axis (y-axis), and

time data on the horizontal axis. Uniform motion is always represented

as a straight line that runs through the plots on a p-t graph.

*using the plots on a graph to determine the line that

generally fits the plots is called a best-fit line

Uniform Motion and Graphing Uniform Motion


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y The slope of a graph refers to whether a line is horizontal or goes up or down

at an angle. There are 3 types of slopes:

- Positive slope

Line slants up to the right.

Indicates the motion is in the direction of the positive y-axis

Position of the object is increasing in the positive direction from

the point of origin

Since the slope is constant, the motion of the object is

travelling in a uniform motion in the positive direction.

- Zero slopeThe object is not moving

This is also an example of uniform motion, since the displacement

of the ball during any time interval is constant.

- Negative slope

Line slants down to the right

Indicates motion is towards the direction of the negative y-

axis, or returning back or past the point of origin.

*This graph displays the

various slopes on a

position-time graph. For

this chapter refer to the

red line. The blue and

green lines will be

explained further in the

summary.

Slope on a position-Time

Positive slo e

Zero slope

Ne ative slo e


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8.2 Average Velocity

y Speed (v) is the distance an object travels during a time interval divided by

the time interval.- Speed is a scalar quantity.

- The SI unit for speed is metres per second (m/s)

- Ex. A toy car travelled 40m in 10s. What was its speed?

40m/10s= 4m/s

y Velocity (v) is the displacement of an object during a time interval divided by

the time interval except

- Velocity describes how fast an objects position is changing- Velocity is a vector quantity and includes direction

- The SI unit for velocity is metres per second (m/s)

- The direction of velocity is the same as the direction of the

displacement or position

- Ex. A toy car travelled 50m [E] in 5s. What is its velocity?

50m [E]/5s= 10m/s [E]

- Objects travelling the same speed can have different velocities simply

because they might be travelling in different directions.

One can have a positive velocity, while the other speed can

have a negative velocity.

- Velocities change when magnitude or direction or both change.

How to use displacement and time intervals to calculate the rate and


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y The slope of a graph represents

rise/run, which is the change in

the y-axis divided by the change

in the x-axis.

y On a position time graph the

slope is the change in position

( d) divided by the change in

time ( t)or the objects average

velocity-v av

y The steeper the slope, the

greater the change in

displacement during the same

time interval. In other words, the object is changing its position quicker in the

same time period.

y To calculate the slope:

- Slope= d

t= df di (final displacement initial displacement)

tf ti (final time initial time)

= 15m 5m

6s 2s

= 10m

4s

= +2.5 m/s- This is the objects average velocity. Because we have included the

direction (+) it is the velocity since velocity is a vector. If we had not

included the direction, and left it as 2.5 m/s, this would become the

objects speed.

Calculating the slope of the Position-Time graph

Rise

Run


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- Also, because it is a position time graph, it automatically becomes

velocity because position is a vector and has direction, making the

answer to the slope a vector as well.

y The slope of a position-time graph represents the objects average velocity.

- positive slope= average velocity is forward

- negative slope= average velocity is backward

- Zero slope= average velocity is zero.

y The relationship between velocity, displacement and time can be described

by the following diagram:

D= displacement

V= velocity

T= time

y It is important to know the difference between velocity and speed

Average Speed= d Average Velocity= d

t t

Ex. A butterfly flies 5m east, 3m south, and 5m west over a time interval of12s.

5m 3m

5m

- Average speed:

13m/12s= 1.08m/s

- Average velocity:

3m [S]/12s= 0.25m/s [S]

Velocity vs. Speed

D

TV

V= D/T

T=D/V

D=VT


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y To convert between m/s and km/h:

- Multiply m/s by 3.6 to convert to km/h m/s 3.6 km/h

- Divide km/h by 3.6 to convert to

- Ex. 85km/h: divide by 3.6= 23.6m/s

- Ex. 72m/s: multiply by 3.6= 259km/h

y To convert between hours and minutes:

- Multiply hours by 60 to convert to minutes

- Divide minutes by sixty to convert to hours

Chapter 9: Acceleration is the rate of change in velocity.

9.1 Describing Acceleration

y An object travelling with uniform motion has equal displacements in equal

time intervals.

y An object travelling with non-uniform motion will:

- Have different displacements during equal time intervals

- Take different amounts of time to travel equal displacements

- Have a continuously changing velocity

y A change in velocity changes when the speed or direction of motion of the

object changes.

y A change in velocity can be calculated by subtracting the initial velocity from

the final velocity.

v= vf vi

Converting Between m/s and km/h

-

Positive and Negative Changes in Velocity


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y Positive changes in velocity:

- If the change in velocity is in the same sign (+/-) as the initial velocity,

the speed of the object is increasing.

Ex. Tom is roller blading down the

street at +8m/s in a forward direction

(+). He is in a hurry so he increases

his velocity to +12m/s. His change in

velocity is

+12m/s (+8m/s) = +4m/s

*The change in velocity is +4m/s in

the forward direction. This means,

Tom was speeding up by 4m/s in the

original direction. His original

forward direction was positive, so his

change in velocity is also positive when he sped up.

y Negative changes in velocity:

- If the change velocity is in the opposite of the initial velocity, the speed

of the object is decreasing.

Ex. Suppose Tom reaches his destination and slows down from +12m/sto +3m/s forward. His change in velocity is

+3m/s (+12m/s) = -9m/s

*The change in velocity is -9m/s opposite the forward motion. In other

words, Tom was slowing down by 7m/s in the original direction. If the

initial forward direction was positive and the change in velocity is

negative the object is speeding up.

y Constant velocity:- Any object travelling with uniform motion in a straight line would have

zero change in velocity.


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y Acceleration (a) is the rate of change in velocity, or how quickly the velocity

of an object is changing.

- Acceleration can be due to a change in speed and/or a change in

direction.- When talking about acceleration, we need to include the magnitude of

the change in the velocity of the moving object and the direction of the

objects velocity- because acceleration and velocity are vectors.

- When comparing the acceleration of two objects, the object with the

greater acceleration changes its velocity in a shorter time interval and

has a greater change in velocity during the same time interval.

Ex. Lets look at the following situation:2 cars, a race car and a beetle, are having a race. Both cars

will be able to reach the speed of

60km/h; however the race car will

be able to reach it faster because of

its powerful engine. In other words, the race car

will be able to change its velocity faster and

therefore will have a greater acceleration, than

the beetle.

*When an object is accelerating the velocity changes and its motion is not

uniform.

y In a straight line motion, acceleration can be either positive or negative, and

is the same as the direction of the change in velocity.

Acceleration

Positive and Negative Acceleration


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y Positive acceleration:

- A car driving along a straight road changes its velocity from 40km/h to

60km/h. the forward motion of the car can be represented as positive

(+). When the cars speed is increasing, the car has a positive

acceleration.

y Negative acceleration:

- Now the car approaches a red light and needs to slow down. The driver

pressed the brakes and the cars speed begins to decrease in a forward

motion. The car now has a negative acceleration.

Velocity

Acceleration

Velocity

Acceleration

If an object is increasing its speed in apositive direction then change in velocity

is positive therefore the acceleration is

positive also.

If an object is decreasing its speed in a

positive direction then the change in

velocity is negative therefore the

acceleration is negative also.


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Velocity

Acceleration

Velocity

Acceleration

*If an object is changing its velocity in the same direction as its initial position then

both the velocity and acceleration is positive, even if it is slowing down.

*If an object is changing its velocity in a different direction than its initial positionthen both the velocity and accelerations is negative, even if it is speeding up.

9.2 Calculating Acceleration

y Acceleration is measured in units of m/s2 (metres per second squred)

y The motion of an object with a changing velocity can be represented on:

- A velocity-time graph

- A position time graph

If an object is increasing its speed in a

negative direction then the change in

velocity is negative therefore the

acceleration is negative also.

If an object is decreasing its speed in a

negative direction then the change in

velocity is positive therefore theacceleration is positive also.


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y The slope of a velocity-time graph is the objects average acceleration.

- Slope= rise/run: when this is calculated on a v-t graph, the answer is the

objects acceleration

- Shows how fast the object is changing its velocity

Velocity-Time graphs

y When the slope on a velocity-time graph is

touching the x-axis at any point, this means

that the object is stationary.

y Zero slopes on a v-t graph mean that the

objects velocity is constant- the object is still

moving but at a constant speed.

y Positive slopes on a v-t graph mean that the

objects velocity is increasing in a positive

direction.

y Negative slopes on a v-t graph mean that

the objects velocity is decreasing in a

positive direction, or increasing in a negative

direction.


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- At slope 1 the

object is at rest

- At slope 2 the

object starts from rest and

increases speed at a

constant velocity

- At slope 3 the

object is traveling in a

positive direction at

constant speed

- At slope 4 the

object is slowing down to a

stop at a constant rate while

still travelling north.

y The relationship between acceleration, change in velocity, and time interval

is given by the following equation:

- a= v

t

Ex. A soccer ball travelling at 6.5m/s towards a fence bounces off at 5m/s. If the

ball was in contact with the fence for 0.20s, what is the balls acceleration?

(Towards the fence is positive)

= (-5m/s 6.5m/s)

0.20s

= -4.0m/s = -20m/s2

0.20s

4

3

1

2

Calculating Acceleration

TA

V


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Ex. A truck starting from rest accelerates uniformly to 18m/s [W] in 4.5s. What is

the trucks acceleration?

= 18m/s

4.5s

= 4m/s2 [W]

= vf-vi

(Refer to the diagram) = tf-ti

Ex. A car accelerates from rest at 3.0m/s2 forward for 5.0s. What is the velocity of

the car at the end of 5.0s?

= (3.0m/s2) (5.0s)

= 15m/s *The cars change in velocity after 5.0s is 15m/s forward so in order to

figure out the velocity we must figure out the change in velocity (initial velocity-

final velocity)

15m/s= vf-0: since the cars initial velocity was zero, the answer remains the same

vf =15m/s

Ex. A train is travelling east at 14m/s. How long would it take to increase its

velocity to 22m/s [E] if it accelerated at 0.05m/s2 [E]?

t = 8.0m/s (calculated by getting the change in velocity)

0.50m/s2

= 16s: It would take the train 16s to increase its speed.

Calculating Changes in Velocity and Time

TA

V


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y Objects near the surface of Earth fall to Earth due to the force of gravity.

- Acceleration due to gravity is 9.8m/s2 downward.

- To analyze situations where objects are accelerating due to gravity

(falling) use the vat triangle shown on the previous page.

Ex. Suppose a rock falls from the top a cliff. What is the change in velocity of the

rock after it has fallen for 1.5s? (Down= (-))

v= (a) ( t)

= (-9.8m/s2) (1.5s)

= -15m/s

*Since down is negative, the change in velocity of the rock is -15m/s

y Air resistance is a friction-like force that opposes the motion of objects that

move through the air.

- If an object is falling, air resistance acts upward on the object

- If air resistance were not present, all objects would fall with the same

acceleration (9.8m/s2) regardless of their shape, size, and mass.

Gravity and Acceleration and Calculating Motion due to Gravity

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