Graphs & Equations of Motion

SAMPLE ONLY SAMPLE ONLY SAMPLE ONLY

For FULL presentation click HERE >> www.warnescience.net

Graphs of Motion

K Warne

http://www.warnescience.net/




Graph Skills

The gradient (slope) of a

straight line graph is

constant and can be

found by taking the

coordinates between

any two points.

The gradient of a curve

changes continually.

At any point the gradient

is found by taking the

gradient of a tangent

to the curve at that

point.

1(x1,y1)

2 (x2;y2)

Grad = y

x

y2 - y1

x2 - x1

=

y

x

1(x1,y1)

2 (x2;y2)

x1

y1

y2

y

x

x

Gradat x =y

x

y2 - y1

x2 - x1

=

y

x

x2





Constant Velocity Example• Assume you walked for 5s covering 1meter every second.

Time (S): 0| 1 | 2 | 3 | 4 | 5 |

X (m): 0| 1 | 2 | 3 | 4 | 5 |

time (s)

Displacement

(m)

Average

Velocity

(m/s)

Instantaneous

Velocity (m/s)

Acceleration

(m/s2)

0 0

1 1

2 2

3 3

4 4

5 5





Velocity vs. time

• Now calculate the GRADIENT and AREA of this graph.

• m = /\y/ /\x = …/… = … m/s2

• Gradient = ……………………..

• AREA = L x b = …. x …. = ….. m (…..)X….

• AREA = …………………………..

v

(m/s)

t (s)

1

50





SKETCH GRAPHS - Constant Velocity

s/(m)

t/(s)

v/(m/s)

t/(s)

GRADIENT = ………..

AREA = …………..

DISPLACEMENT - TIME Graph

VELOCITY - TIME Graph

The ……………… between any two

points on the VELOCITY - TIME

graph equals the objects

displacement between the two

points.

t1 t2

1.

2.

The ……………………of the

DISPLACEMENT vs TIME

graph equals the velocity of

the object. (at any point)

1. 2.

... . . . . . . . . . . . . . . . . . . . . . . . . . .. . ....

time/(s) 0 1 2 3 4 5 6 7 8 9 10

1 2S1 S2

s1

s2

..

.

Displacement increases by same

amount in equal time intervals.





Constant Acceleration

• Assume you started from rest but traveled further every second.

Time (S): 0| 1 | 2 | 3 | 4 | 5 |

S (m): 0| 0.5| 1.5 | 2.5 | 3.5 | 4.5 |

t(s) X (m) Vav Vi a

1 0.5

2 2

3 4.5

4 8

5 12.5

Calculate

• aV -Average

velocity

• Instantaneous

velocity

• Acceleration






0

2

4

6

8

10

12

14

0 2 4 6

s

0

1

2

3

4

5

6

0 2 4 6

Vi

0

0.2

0.4

0.6

0.8

1

1.2

0 2 4 6

a

Gradient (3.5s)

= R/R = (14-0)/(5.8-1.9)

= 3.6 m/s

= velocity at 3.5s

Gradient = R/R = 6/6

= 1.0 m/s2 =

acceleration

Area = l x b

= 5 x 1

= 5 m/s

= change in

velocity!





SKETCH GRAPHS - Constant ACCELERATION

s/(m)

t/(s)

v(m/s)

t/(s)

GRAD = ….

DISPLACEMENT - TIME VELOCITY - TIME

t/(s)

GRAD = …

t2t

ACCELERATION - TIMEa

(m/s2)

The gradient of the displacement vs

time graph (tangent - at any point)

gives the ……………..of the object

at that point.

The gradient of the velocity vs

time graph (at any point) gives

the ……………….of the object.

.... . . . . . . . . . .

time/(s) 0 1 2 3 4 5 6 7 8 9 10

1 2S1 S2

t1

s1

Displacement increases by (uniformly ) increasing amounts in

equal time intervals.

s2





.

Graphs of MotionA - acceleration (+)

B - constant velocity (+)

C - deceleration (+)

D - stationary

E - reverse acceleration (-)

F - reverse constant v (-)

G - reverse deceleration (-)

t

t

t

s

a

A

B

C DE

F

G

v

... . . . . . . .

. . . . . . . .

. . . . . . . ...

. . . . . ..

. . . . . . . . .

... . . . . . . .





.

........................................ . . . . . . . .

SKETCH GRAPHS - Displacement vs Time

s/(m)

t/(s)

Constant Velocity

Displacement changes by

same amount every second.

s/(m)

t/(s)


Increasing displacement per

second - velocity increases.

s

(m)

t/(s)

Stationery Object

Displacement

remains constant.

Displacement

is being reduced (coming

back to start).

s

(m)

t/(s)

Object moves backwards.

............................

s

(m)

t/(s)

Deceleration.

Rate of increase in

displacement decreases -

slowing down.

. . . . ....





SKETCH GRAPHS - Task

s/(m)

t/(s)

v/(m/s)

t/(s)

Draw sketch graphs of displacement vs time, velocity vs

time and acceleration vs time for a car that starts off

from rest, accelerates uniformly for 5s, attains a speed

of 30m/s which it maintains for 10s. The car then slows

down for 15s at which point it comes to a halt. Indicate

as much detail on the graphs as possible.

a/(m/s2)

t/(s)





SKETCH GRAPHS - Example

Tut on Graphs & equations

0 10 20 30 40

8

12

|





Tut on Graphs & equations

0 10 20 30 40

8

-12

|

constant

velocityslowing

down

(decelerating

uniformly)

speeding

up reverse

uniform acceleration

negative direction

slowing (decelerating)

down backwards

constant

velocity

accelerating

forwards

constant

velocity

V





Graphs of two motions.The graph shows the

speeds of two cars A & B as a function of time.

1. What is the difference in the distances traveled by A & B after 20 s? (7)

2. After how many seconds will A & B have traveled the same distance? (6)

3. Calculate the acceleration of A. (4)

B

A

1510

5

6

v

t (s)20





Graphs of Vertical MotionAn object is thrown vertically up and returns to the thrower’s hand.

0

10

20

30

V

(m/s)

0

-10

-20

-30

0

-10

-20

-30

30

20

10

X

tt t

V a





Hi -

This is a SAMPLE presentation only.

My FULL presentations, which contain a lot more more slides and other resources, are freely

available on my resource sharing website:

www.warnescience.net(click on link or logo)

Have a look and enjoy!

WarneScience






Education

Graphs & Equations of Motion