speed velocity accelerationfaculty.ric.edu/phys110/lecture notes - kinematics.pdfspeed velocity...
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Speed
Velocity
Acceleration
A scalar is a quantity which has the magnitude only (mass, length, time,
volume, temperature).
A vector is a quantity which has both the magnitude and direction (velocity,
force).
In physics we use System International (SI) units.
2
In physics we need vectors because the real world is three dimensional.
System International or the metric system is used in all countries aside from
the USA; here the British System is in use.
1. Length: the meter (m) [1 ft = 0.305 m, 1 inch = 2.54 cm= 2.54!10-2 m]
2. Mass: the kilogram (kg) [1 slug = 14.9 kg]
3. Time: the second (s) [the same as in British System]
Mechanics and Forces
3
1. Time (second " s)
2. Distance (meter " m )
3. Speed (m/s)
4. Velocity (speed and direction)
9. Torque (N·m)
5. Acceleration (m/s2)
6. Force (newton " N)
10. Linear momentum (kg·m/s)
7. Kinetic, potential energy, and work (joule " J)
8. Power (watt " W)
12. Frequency (hertz " Hz)
11. Angular momentum (kg·m2/s)
Motion with Constant Velocity and Constant Acceleration
Constant velocity:
- Equal distance covered in equal time intervals:
4
Question: How we can describe motion with
constant velocity and acceleration?
Constant acceleration:
- Equal increments of speed gained in equal time intervals;
- Distance increases in each time interval.
Horizontal Motion at Straight Line
5
# We want to understand how objects are moving, so we will:
- discuss various types of motion;
- calculate parameters of motion.
# For motion we will use the following quantities:
Distance, time, speed, velocity, and acceleration.
Using the total distance and the total time we can find the average speed.
We also can find the average speed using change in distance and change in time.
Total distance (dtotal ) = dfinal - dinitialTotal time (ttotal ) =
= tfinal - tinitial
initialinitialdt , finalfinal dt ,
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Average and Instantaneous Speed
t
d
tt
ddv
initialfinal
initialfinal
av!
!=
"
"=
timetotal
distance total speed average =
interval short timevery
distancein change speed ousinstantane =
shortvery
instt
dv
!
!=
The unit of speed in the System International: m/s
Average speed, vav
Instantaneous speed, vinst
in time change
distancein change speed average =
total
total
av
t
dv =
av
total
total
v
dt =
totalavtotaltvd =
7
A car was traveled during 1 and 3 hours.
hkmvhkmv
htht
/40,/60
3,1
21
21
==
==
Find the average speed.
total
total
av
t
dv =
kmhhkmtvd 60)1)(/60(111 ===
hkmvav
/45=
Average Speed
1. Equation used:
3. Answer:2. Solution:
hkmh
km
t
dv
total
total
av/45
4
180===
hhhttotal
431 =+=
kmkmkmdddtotal
1801206021
=+=+=
kmhhkmtvd 120)3)(/40(222 ===
Speed and Velocity
8
# Speed is just a positive number (speed is a scalar).
# Velocity has the magnitude (a number) and the direction (velocity is
a vector).
# For speed we need to know only the number.
# For velocity we need to know both the magnitude and direction.
Speed
Velocity
If an object is moving, we
can use quantities “speed”
and “velocity”.
The speedometer of the truck #1 moving to the east reads 90 km/h. It passesanother truck, # 2, that moves to the west at 90 km/h.
1) Do both trucks have the same speed?
2) Do they have the same velocity?
3) What speed we are reading on the speedometer:
average or instantaneous?
Speed and Velocity
Yes No
Yes No
# 1
# 2
9
Instantaneous
Average
Motion with Constant Speed: Graphs
10
t
v1) Speed vs. time
It’s important to understand how we can show a motion using graphical method.
initialt
t!
d!
finalt t
initiald
finald
d 2) Distance vs. time
constvt
d==
!
!=
in time change
distancein change
t
dv =
Speed = const
Speed = const
0
vtd =v
dt =
DistanceSpeed Time
t
v
tt
vva
initialfinal
initialfinal
av!
!=
"
"=
11
in time change
yin velocit change on accelerati =
The unit of acceleration in the System International: m/s2
Acceleration shows how fast an object changes its velocity.
Acceleration
Acceleration during motion along straight line:
If an object is moving with constant velocity, acceleration is equal zero:
00
=!
="
"=
ttt
vva
initialfinal
initialfinal
av
12
v
v!
t! t
t
v
tt
vva
initialfinal
initialfinal
av!
!=
"
"=
Positive and Negative Acceleration
Positive acceleration: velocity increases with the time.
Negative acceleration: velocity decreases with the time.
v
v!
t! t
t
v
tt
vva
initialfinal
initialfinal
av!
!"=
"
"=
finalfinal tv ,
initialinitialtv ,
initialinitialtv ,
finalfinal tv ,
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Equations for Horizontal Motion at Straight Line
Acceleration is constant, velocity is changing:
Acceleration is zero, velocity is constant:
vtd = time-velocity,- distance, tvd !
2
2at
tvdinitial
+=
2
finalinitial
av
vvv
+=
2
2at
d =
Average velocity (speed):
Distance (accelerate from the rest):
Velocity (speed) after time t: atv =
Distance (accelerate while moving at
constant speed):
v
dt =
t
dv =
Motion at Constant Acceleration: Graphs
14
d
t
a
t
v
t
atv =
consta =2
2at
d =
1) Acceleration
2) Speed
3) Distance
Find the distance traveled by the car
for 4 s if it started to move from the
rest at the acceleration of 3 m/s2.
2
2at
d = mssm
242
)4)(/3( 22
==
d Distance vs. time
0
1) Car B moves faster
2) Car A moves faster
3) Both cars have the same speed
4) Note enough data
t
Distance vs. Time
15
Graph below shows distance vs. time for moving cars, A and B.
Which answer is correct?
A
Bt
dv =
The slope of the distance vs. time graph is the speed.
vtd =
1t
vSpeed vs. time
0
1) Acceleration of car B is larger
2) Acceleration of car A is larger
3) Both cars have the same acceleration
4) Note enough data
t
Speed vs. Time
16
Graph below shows speed vs. time for two moving cars, A and B.
Which answer is correct?
A
B
t
va =
The slope of the speed vs. time graph is the acceleration.
atv =
1t
A car was traveled at the average speed of 5 m/s for 1 hour. The
distance traveled by the car is:
Speed and Time
1) 0.3 km
2) 3 km
3) 18 km
4) 1.8 km
17
kmmssmvtd 1800018)6060)(/5( ==!==
vtd =
50 kg are equal:
Conversion
1) 5!103 g
2) 5!10-3 g
3) 5!10-4 g
4) 5!104 g
18
ggkg 43105105050 !=!=
ggkg 31010001 ==
19
Relative Velocity
v=8 m/sv=2 m/s
8 m/s 2 m/s=
6 m/s
Sometimes an object has two velocities at the same time. Let’s say a
person is walking on the train at 2 m/s in the opposite direction of the
train’s motion at 8 m/s.
How fast this person is going relative to someone on the ground?
We will use vector’s addition:
EastWest
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