# UAM

```Unit 4 – Module 1
Uniform Accelerated Motion
The Cheetah: A cat that is built for speed. Its strength and
agility allow it to sustain a top speed of over 100 km/h. Such
speeds can only be maintained for about ten seconds.
Photo © Vol. 44 Photo Disk/Getty
Uniform Acceleration
in One Dimension:
• Motion is along a straight line (horizontal, vertical
or slanted).
• Changes in motion result from a CONSTANT force
producing uniform acceleration.
Distance and Displacement
Distance is the length of the actual path taken
by an object. Consider travel from point A to
point B in diagram below:
s = 20 m
A
B
Distance s is a scalar
quantity (no direction):
Contains magnitude only
and consists of a
number and a unit.
(20 m, 40 mi/h, 10 gal)
Distance and Displacement
Displacement is the straight-line separation of
two points in a specified direction.
D = 12 m, 20o
A
q
B
A vector quantity:
Contains magnitude
AND direction, a
number, unit & angle.
(12 m, 300; 8 km/h, N)
Distance and Displacement
• For motion along x or y axis, the displacement is determined
by the x or y coordinate of its final position. Example:
Consider a car that travels 8 m, E then 12 m, W.
Net displacement D is
from the origin to the
final position:
D = 4 m, W
What is the distance
traveled? 20 m !!
D
8 m,E
x = -4
x
x = +8
12 m,W
Definition of Speed
•Speed is the distance traveled per unit of
time (a scalar quantity).
d = 20 m
A
Time t = 4 s
B
v=
d
t
=
20 m
4s
v = 5 m/s
Not direction dependent!
Definition of Velocity
•Velocity is the displacement per unit
of time. (A vector quantity.)
s = 20 m
A
D=12 m
20o
Time t = 4 s
B
D 12 m
v 
t
4s
v = 3 m/s at 200 N of E
Direction required!
Examples of Speed
Orbit
2 x 104 m/s
Light = 3 x 108 m/s
Jets = 300 m/s
Car = 25 m/s
Speed Examples (Cont.)
Runner = 10 m/s
Glacier = 1 x 10-5 m/s
Snail = 0.001 m/s
Acceleration
•Acceleration is a measure of how
fast velocity changes.
Acceleration is the change of
velocity divided by the change of
time. Acceleration is a vector,
and therefore includes both a
size and a direction.
Example of Acceleration
•An object was moving north at 10
meters per second. The object speeds
up and now is moving north at 15
meters per second. The object has
accelerated.
•Jane is walking east at 3 kilometers per
hour. Jane's velocity does not change.
Jane's acceleration is zero.
Review of Symbols and Units
•Displacement (x, xo); meters (m)
•Velocity (v, vo); meters per second (m/s)
•Acceleration (a); meters per s2 (m/s2)
•Time (t); seconds (s)
Review sign convention for each symbol
Uniformly Accelerated Motion
•A body has a uniformly
accelerated motion if it travels
in a straight line and its
velocity increases by equal
amounts in equal interval of
time
Formulas
• A.
• B.
𝑣𝑓= 𝑣𝑖 + 𝑎𝑡
𝑣𝑎𝑣𝑒= 𝑣𝑓+𝑣𝑖
2
• C.
• D.
𝑎= 𝑣𝑓−𝑣𝑖
𝑡
d= (𝑣𝑓+𝑣𝑖) 𝑡
2
• E.
d= 𝑣𝑖𝑡 + 0.5𝑎𝑡2
• F
Sample Problem no. 1
•The brakes of a car provides an
acceleration of -5.0 m/s2. How
long will it take for a car
travelling at 20. 0 m/s to stop?
Sample Problem no. 2
•A truck starts from rest and
accelerates at 2.0 m/s2 for 4.0 s.
How far will it go at the end of this
time?
•An airplane from rest accelerates on a
runway at 5.50 m/s2 for 20.25 s until it
finally takes off the ground. What is
the distance covered before takeoff?
•A jeepney from rest accelerates from
uniformly over a time of 3.25 seconds
and covers a distance of 15 m.
Determine the acceleration of the
jeepney.
• A car covers 200.0 m while increasing
its velocity from 20.0 m/s to 30.0 m/s.
Compute for acceleration
•Starting from rest, a car
accelerates at 2.0 m/s2. How
far will it go after 6.0 s?
•A train accelerates to a speed of 20
m/s over a distance of 150 m.
Determine the acceleration (assume
uniform) of the train.
```
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