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GENERAL CONCEPTS OF MOTION
Speed - scalar
quantity that refers to how fast an object is moving.
-
Amount of distance travel d per unit time t.
Speed
(v) = d/t
Velocity (v) – a
vector quantity
-
The rate at which object changes its position
-
m/s (SI unit)
-
amount of displacement traveled (d)
per unit time t
Velocity (v) = d/t
Average speed and Average velocity
Average speed – the total distance traveled divided by the
total time, independent of the direction
vave
= dT/t
Average Velocity – total displacement divided by time
vave = d/t
Example:
A car traveled 400.okm to the north. It turned and traveled
100.0km due east. Then, it turned
northwest and traveled 250.0km. Finally, it turn and traveled 200.0km to the
south. If the entire trip is 10.0 hrs: (a)
What is the car’s average speed? (b) What is the average velocity
Given:
d1 = 400.0km
due north
d2= 100.0km
due east
d3= 250.0km
due northwest
d4= 200.0km
due south
t=10.0h
(a)
Average speed
vave = dT/t
compute for the total distance (dT)
dT
=
d1+d2+d3+d4
= 400.0 + 100.0 + 250.0km +200.0km
= 950.0km
Compute for the average speed (vave
)
vave = dT/t =
950.0km/10hr = 95.0km/hr
(b)
Average Velocity
Since
it is a vector quantity, we need to use addition of vector
vave
= dT/t ,
first ween need to compute for total displacement
Total
Displacement: (dT)
Sketch:
Get summation of each axis
|
X
|
Y
|
d1
|
0
|
400km
|
d2
|
100km
|
0
|
d3
|
-250cos45˚ = -176.8km
|
250sin45˚ = 176.8km
|
d4
|
0
|
-200km
|
|
∑dx = -76.8km
|
∑dy= 376.8km
|
Constant
and instantaneous speed and velocity
·
An object is saild to have no constant
speed if it neither speeds-up or slows-down
·
An object is said to have constant
velocity if it has constant speed and constant direction
Instantaneous
speed - the speed of an object at one
particular moment in time
Instantaneous
velocity – the velocity of an object at one particular moment in time
Example:
A
car entered a bridge at 2:45pm and exited at 5:15pm. If the bridge is 105km
long and the car traveled at constant speed across the bridge, what is the
speed of the car at 4:00pm?
Solution:
Given:
D = 105km
t= 2:45pm
to 5:15pm = 2h 30 min = 2.5hr
Get
the constant speed
v = d/t =
105km/2.5hr = 42km/hr
v4:00 = 42km/hr
There
is an acceleration if:
a.
The speed is changing
b.
The speed is constant but the direction
is changing
c.
The speed and direction are both changing
Example:
An
object uniformly accelerates from 3.0m/s to 15.0m/s in 4.0s. There is no change
in the direction of motion. Find (a) the acceleration and (b) the displacement
traveled.
In
two dimensions
A
car is heading to the north and then smoothly made a westward turn; hence, it
is now heading to the west. During the travel, the speed of the car remains
constant at 1.5km/h. What is the acceleration of the car? The total travel time
of the car as it smoothly changed its direction is 15min.
To add the velocity vectors:
|
X
|
Y
|
vf
|
0
|
-1.5km/h
|
vi
|
-1.5km/h
|
0
|
|
-1.5km/h
|
-1.5km/h
|
DECELERATION:
Is an acceleration that is
directed towards the direction opposite that of velocity
Example:
An object slow down from 23.0m/s
due east to 5.0m/s due east. What is the acceleration? Indicate its direction.
