Kinematics in One Dimension
Monday, September 9, 13
Motion
The development of a precise mathematical formalism for
the description of motion is one of the most important steps
forward in the history of science.
Monday, September 9, 13
Motion
The development of a precise mathematical formalism for
the description of motion is one of the most important steps
forward in the history of science.
x(t)
Monday, September 9, 13
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Monday, September 9, 13
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
vavg =
x
51 km
=
t
1 min
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Monday, September 9, 13
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
vavg =
x
51 km
=
t
1 min
51, 000m
=
= 850 m/sec
60 sec
Monday, September 9, 13
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
vavg =
x
51 km
=
t
1 min
51, 000m
=
= 850 m/sec
60 sec
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Armavir radar station detected two ballistic missiles launched from the centre of the Mediterranean
sea at 10:16 AM, on Sep 3, 2013. The station is situated about 1,000 km away.
How many seconds before it was detected the missile was actually launched.
hint: a radar is a pulse of radiowaves.
Monday, September 9, 13
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
vavg =
x
51 km
=
t
1 min
51, 000m
=
= 850 m/sec
60 sec
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Armavir radar station detected two ballistic missiles launched from the centre of the Mediterranean
sea at 10:16 AM, on Sep 3, 2013. The station is situated about 1,000 km away.
How many seconds before it was detected the missile was actually launched.
hint: a radar is a pulse of radiowaves.
vavg = 300, 000 km/sec
Monday, September 9, 13
Average Velocity
The AIM-7 Sparrow missile covers 51km in a minute, what
is its average speed in meters per second?
x
51 km
=
t
1 min
vavg =
51, 000m
=
= 850 m/sec
60 sec
A U.S. Air Force F-15 Eagle fires an AIM-7 Sparrow missile in
January 2005. Source: Wikipedia.
Armavir radar station detected two ballistic missiles launched from the centre of the Mediterranean
sea at 10:16 AM, on Sep 3, 2013. The station is situated about 1,000 km away.
How many seconds before it was detected the missile was actually launched.
hint: a radar is a pulse of radiowaves.
vavg = 300, 000 km/sec
t=
x
vavg
Monday, September 9, 13
2, 000 km
=
= 6 ⇥ 10
300, 000 km/sec
3
sec
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
x(t)
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
x(t)
t
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
x(t)
v(t)
t
Instantaneous Velocity
The instantaneous velocity
is the rate of change of the
position at any moment of
time. In other words, it is
the derivative of the
position function which is
its slope.
dx(t)
v(t) =
dt
Monday, September 9, 13
x(t)
v(t)
t
Average Acceleration
A 747 airliner reaches its takeoff
speed of about 280 km/hr in 35
seconds. What is the average
acceleration?
Monday, September 9, 13
Average Acceleration
A 747 airliner reaches its takeoff
speed of about 280 km/hr in 35
seconds. What is the average
acceleration?
vtake
off
= 280 km/hr ⇥
= 77.8 m/s
Monday, September 9, 13
✓
1000 m
km
◆
⇥
✓
hr
3600 s
◆
Average Acceleration
A 747 airliner reaches its takeoff
speed of about 280 km/hr in 35
seconds. What is the average
acceleration?
vtake
off
= 280 km/hr ⇥
✓
1000 m
km
◆
⇥
= 77.8 m/s
aavg =
v
vtake off
=
t
t
= 2.3 m/s
Monday, September 9, 13
2
0
78 m/s
=
35 s
✓
hr
3600 s
◆
Instantaneous Acceleration
The instantaneous acceleration is the rate of change of the
velocity at any moment of time. In other words, it is the
derivative of the velocity function which is its slope.
dv(t)
a(t) =
dt
Monday, September 9, 13
Instantaneous Acceleration
The instantaneous acceleration is the rate of change of the
velocity at any moment of time. In other words, it is the
derivative of the velocity function which is its slope.
dv(t)
a(t) =
dt
Monday, September 9, 13
Instantaneous Acceleration
The instantaneous acceleration is the rate of change of the
velocity at any moment of time. In other words, it is the
derivative of the velocity function which is its slope.
dv(t)
a(t) =
dt
Monday, September 9, 13
G-Forces
Monday, September 9, 13
G-Forces
G-Force is the acceleration an object
feels in units of g = 9.8m/s^2 which
is Earth’s gravitational acceleration
on the surface of the Earth. It is a
useful unit because we all have an
intuitive sense of the acceleration
involved, but it is not an MKS unit.
e.g.
3 g = 3 x 9.8 m/s^2
= 29.6 m/s^2
Monday, September 9, 13