07 Kinematics - Motion Graphs - SJHS-IB-Physics

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14 Νοε 2013 (πριν από 3 χρόνια και 10 μήνες)

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Kinematics

Motion Graphs

Motion Graphs

1. Displacement


Time graphs






a = uniform positive velocity

b =

c =

d =

Displacement

Time

a

b

c

d

a = uniform positive velocity

b = decreasing velocity

c = at rest

d = uniform negative velocity

The gradient of a displacement
-

time graph is equal
to the velocity of the object at any instant.

gradient =

Δ
y

=
Δ

displacement
=
Δ
s

= velocity



Δ
x
Δ

time


Δ
t

Instantaneous velocity is given by the gradient of
the
tangent

to the line at a certain time, t.


Δ
y

Δ
x

time

displacement

t

v = m =
Δ
y



Δ
x


2. Velocity


Time graphs






a = uniform positive
acceleration

b =

c =

d =


Velocity

Time

a

b

c

d

a = uniform positive
acceleration

b = non uniform positive
acceleration

c = uniform velocity

d = uniform negative
acceleration (perhaps a
deceleration)

The gradient of a velocity
-

time graph is equal to
the acceleration of the object at any instant.

gradient =

Δ
y

=
Δ

velocity

=
Δ
v

= acceleration



Δ
x
Δ

time


Δ
t

Instantaneous acceleration is given by the gradient
of the
tangent

to the line at a certain time, t.


The area under any section of a v
-
t graph is equal
to the total displacement over that time period. (So
you could have a negative area, indicating negative
displacement)

area =
average
velocity x time = v x
Δ
t =
Δ
s

3. Acceleration


Time graphs

We are mainly interested in uniform acceleration:






a = uniform positive
acceleration

b = uniform negative
acceleration

Acceleration

Time

a

b

Bouncing Balls

Q.

Two masses follow the paths shown. By sketching
a velocity time graph for each, determine which one
will reach the end of the track first?

A

B

v

t

v

t

A. They both travel the same total distance,
therefore the area under the v
-
t graph must be the
same. Thus ball B must reach the end first!

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