Motion

KINEMATICS

Quantity in motion

distance/displacement

speed/velocity

Acceleration/deceleration

Distance and displacement

Distance: the length of the path between two point.

Displacement: The straight distance from the initial position to final position.

The change in position.Displacement is the straight distance

in a specified direction.

scalar

vector

A B

r

Speed and velocity

takentime

movedcedisspeed

_

_tan

takentime

ntdisplacemevelocity

_

scalar

vector

Instantaneous speed and average speed

Instantaneous Speed - speed at any given instant in time.

Average Speed - average of all instantaneous speeds; found simply by a distance/time ratio.

Acceleration

takentime

velocityofchangeonaccelerati

_

__

t

uv

The rate of change in velocity.

deceleration

The definition of acceleration means that something is accelerating if its velocity changes,

Since velocity includes speed and direction,

Then something is accelerating if its speed, its direction or both change.

Distance—time graph for object moving in a uniform speed

D-t graph for two objects moving in uniform speed, VA>VB

D-t graph for a object moving in a uniform acceleration

Velocity—time graph for a object moving in a uniform acceleration

V-t graph for two objects moving in uniform acceleration, aA>aB

continued There are three parts

to the journey shown on the left.

Moving at a steady speed, slowly

Not moving for quite some time

Moving again, but at higher speed .

VE

LOC

ITY

A Road test report gives the following data for a standing start acceleration test on a Car:

t/s 0 5 10 15 20 25 30 35 40

v/(m/s) 0 14 24 30 34 37 39 40 40

(a)Draw a velocity-time graph for the test.

(b)What is the displacement of the car when it has reached a speed of （Ⅰ） 25m/s ( ) 35m/sⅡ

(c) Find （Ⅰ） the acceleration of the car when its speed is 30m/s ( ) the car’s maximum accelⅡeration

A

B

CD

E

A: acceleration B: faster constant speed C: deceleration D: stationary E: slower constant speed

continued Describe three parts to

the journey shown on the left.

Moving at a steady acceleration, slowly

Moving at a constant velocity

Accelerating, but at higher acceleration .

VE

LOC

ITY

V-t Graphs for the sky-diver

With parachuteAir resistance can’t be ignored.

The horizontal velocity is negligible.

The forces on the sky-diver

The parachutist is now falling fast enough for the air resistance to equal her weight.

This means that the forces on her are in balance, so her speed stops increasing and stays constant - she has reached her terminal velocity.

Terminal Velocity

V-t Graphs for the sky-diver

As part of an aerobatic display, a skydriver jumps out of an aeroplane and falls towards the ground. She does not open her parachute until she reaches her terminal velocity.

(i) Explain why she reaches a terminal velocity.

(ii)Given that she can not change her height during the fall, explain how she could reach a higher terminal velocity.

Describe and explain what is happening between 40s and 60s.

She could make her shape more streamline in order to reduce her air resistance.

(Around 200km/h in this position - he can fall faster if he leans forward to go head first.)

Terminal Velocity

Terminal Velocity---- dragonfly

Terminal Velocity

Terminal Velocity

How to measured instantaneous distance and speed?

Question 1.16Ultrasonic displacement sensorData-logger

Light gate

Motion Graph

Formula

time

Velocit

y

u

v

t

We can know the acceleration of the object by calculating the slope (gradient).

t

uvonaccelerati

1

t

uvonaccelerati

)2( atuv

time

Velocit

y

u

v

t

We can know the displacement of the object in time t by calculating the area under the graph.

)3(2

tvu

S

)4(2

vu

v

time

Velocit

y

u

v

t

utS 1

tuv

S22

21 SSS

t

uva

tuv

utS2

atuv

)5(2

1

22

atuttat

utS

t

uva

)3(2

tvu

Sa

uvt

a

uv

a

uvvuS

22

22

)6(2 22 uvaS

)1(

t

uva )2( atuv

)3(2

tvu

S )4(2

vu

v

)5(2

1 2 atutS

)6(2 22 uvaS

MOTION GRAPHS.

If something is moving at a steady speed, it means we expect the same increase in distance in a given time.

Time is increasing to the right, and distance is increasing steadily time. It moves at a

steady speed.

CONSTANT SPEED. Both the lines below

show that each object moved the same distance but the steeper yellow line got there before the other one.

A steeper gradient indicates a larger distance moved in a given time. In other words, higher speed.

DISTANCE-TIME GRAPH SHOWING ACCELERATION.

The line below is curving upwards. This shows an increase in speed, since the gradient is getting steeper.

In other words, in a given time, the distance the object moves is larger. It is accelerating..

V-t graph

Velocit

y

What’s motion for this object?

Describe these two motion .

VE

LOC

ITY