motion along a straight line [PDF]

'distance' = total ground covered while traveling, e.g. odometer reading ... e.g. driving a car along a long straight st

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Idea Transcript


motion along a straight line

physics 111N

“displacement” & “distance” ➜ we need to be a bit pedantic here: ➜ ‘distance’ = total ground covered while traveling, e.g. odometer reading ➜ ‘displacement’ = vector from where you started to where you end up displacement sign indicates the direction & distance = 10 m

but distance = 10 m physics 111N

2

“displacement” & “distance” ➜ displacement and distance can be quite different displacement

distance = 8m + 6m + 8m = 22m

‘vector’ sum (sum with signs) physics 111N

3

average velocity ➜ just the displacement divided by the time taken

e.g. driving a car along a long straight stretch of road

00:26:05

physics 111N

00:30:17

4

average velocity ➜ suppose we go the other way (but define the x-axis the same way)

01:42:05

01:33:88

negative sign means opposite the axis direction

physics 111N

5

average & instantaneous velocity ➜ let’s make a plot of the position of an object as a function of time

physics 111N

6

average & instantaneous velocity ➜ compute the average velocity between t = 1.00 s & t = 5.00 s

physics 111N

7

average & instantaneous velocity ➜ compute the average velocity between t = 2.00 s & t = 5.00 s

physics 111N

8

average & instantaneous velocity ➜ compute the average velocity between t = ? & t = 5.00 s

? is this getting closer to the slope of the curve at t=5s ? physics 111N

9

average & instantaneous velocity ➜ compute the average velocity between t = ? & t = 5.00 s

as Δt→0, we approach the slope of the curve physics 111N

10

instantaneous velocity ➜ the velocity “at an instant in time” is defined to be and we just saw that it corresponds to the slope of the x-t curve

physics 111N

11

instantaneous velocity

“moving to larger x”

physics 111N

“not moving”

“moving to smaller x”

12

acceleration ➜ if an object’s velocity changes, it has undergone an acceleration ➜ we can define average acceleration

e.g. driving a car along a long straight stretch of road

00:00:00

00:05:50

positive sign means velocity is increasing physics 111N

13

acceleration - meaning of the sign

physics 111N

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acceleration - meaning of the sign

so be careful, the sign of the acceleration doesn’t just mean speeding up / slowing down physics 111N

15

instantaneous acceleration ➜ we define instantaneous acceleration which is the slope of the v-t curve

v��m�s� 15 10 5

1

physics 111N

2

3

4

t�s

16

instantaneous acceleration

physics 111N

17

motion with constant acceleration ➜ simple, but very important, example of a particle being accelerated @ t=0, velocity = v0 @ t, velocity = v v

a

t

t

➜ the constant (positive) acceleration is causing the velocity to increase at a constant rate e.g. if a=+10 m/s2, in 1 sec, v increases by 10 m/s in another 1 sec, v increases by another 10 m/s ... physics 111N

18

pedal to the metal ➜ suppose you’re driving on the highway at 17 m/s and you press the accelerator to accelerate at a constant 3.0 m/s2. After 3.0 seconds, what is your speed?

physics 111N

19

position at constant acceleration ➜ we’d like to get an equation for the position as a function of time we can figure it out (“derive” it) first a simpler example - constant velocity v

x

t

t

v

notice that the change in x is the area under the v-t graph

area = v×t t

physics 111N

20

position at constant acceleration ➜ it is generally true that the change in position is the area under the v-t graph v

constant acceleration

a

t

t

v

area = ½(v-v0)t total area = ½(v+v0)t area = v0t t

physics 111N

21

position at constant acceleration ➜ it is generally true that the change in position is the area under the v-t graph v

constant acceleration

a

t

t

x

t physics 111N

x-t curve is a parabola 22

formulas for constant acceleration ➜ probably useful for you to remember the following equations

physics 111N

23

entering the freeway A sports car is sitting at rest on a freeway entrance ramp.The driver sees a break in traffic and floors the gas pedal, so that the car accelerates at a constant 4.9 m/s2 as it moves in a straight line onto the freeway. What distance does the car travel in reaching a freeway speed of 30 m/s ?

define ←solve for this

physics 111N

24

pursuit A motorist traveling at a constant velocity of 15 m/s passes a school-crossing corner where the speed limit is 10 m/s. A police office on a motorcycle stopped at the corner starts off in pursuit with constant acceleration of 3.0 m/s2. How much time elapses before the officer catches up with the car ?

POLICE

physics 111N

CAR

we want to know when the POLICE and the CAR are at the same location

25

pursuit

POLICE

physics 111N

CAR

we want to know when the POLICE and the CAR are at the same location

26

pursuit 2 - the panicking motorist A motorist traveling at a constant velocity of 15 m/s passes a school-crossing corner where the speed limit is 10 m/s. A police office on a motorcycle stopped at the corner starts off in pursuit with constant acceleration of 3.0 m/s2. This time the motorist sees the cop and applies the brakes as he passes the corner, causing a constant acceleration of -2.0 m/s2. How much time elapses before the officer catches up with the car ?

POLICE

physics 111N

CAR

we want to know when the POLICE and the CAR are at the same location

27

free fall if we neglect the effect of air, objects dropped or thrown vertically up or down accelerate at a constant rate objects accelerate toward the center of the Earth due to gravity, which we’ll explore later in this course

now just because I tell you this, doesn’t mean it is true ! - it’s a theory that needs to be tested by doing experiments

physics 111N

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free fall experiment - is the acceleration constant ? high-speed photography of a ball falling in a vacuum chamber - a shot every Δt seconds measure how far the ball has travelled in each Δt seconds

y

for constant acceleration, should increase linearly with t

Δy �y

the data suggests constant acceleration

with precise measurements, t we find |a| = 9.80 m/s2 physics 111N

29

free fall turns out all objects accelerate at the same rate e.g. drop an apple versus drop a feather “no way!”, you’d say, “a feather will float downwards, an apple will drop” true, but this is a property of the air surrounding the feather remove the issue of air resistance - do the experiment in vacuum

or a somewhat more expensive experiment ... physics 111N

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free fall - hammer & feather on the moon

physics 111N

31

pumpkin drop Suppose you were to drop a pumpkin from the top of a 40m high building. Neglecting air resistance, how long does it take for the pumpkin to reach the ground and how fast is it moving when it gets there ?

moment of release

reaches ground

at all times

physics 111N

32

pumpkin throw Suppose you were to throw a pumpkin vertically upward from the top of a 40m high building at 10 m/s. Neglecting air resistance, what is the maximum height above the ground reached by the pumpkin and how long after release does it reach this point ? When does the pumpkin reach the ground ?

moment of release

highest point

at all times

physics 111N

33

pumpkin throw Suppose you were to throw a pumpkin vertically upward from the top of a 40m high building at 10 m/s. Neglecting air resistance, what is the maximum height above the ground reached by the pumpkin and how long after release does it reach this point ? When does the pumpkin reach the ground ?

moment of release

highest point

at all times

physics 111N

34

pumpkin throw Suppose you were to throw a pumpkin vertically upward from the top of a 40m high building at 10 m/s. Neglecting air resistance, what is the maximum height above the ground reached by the pumpkin and how long after release does it reach this point ? When does the pumpkin reach the ground ?

moment of release

reaches the ground

solve a quadratic ! at all times

physics 111N

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