Transcript Speed, Velocity and Acceleration 927

Speed, Velocity & Acceleration
9/27/10
Position vs Distance
• Position is an objects location compared
with where it started, including direction
• Distance is a length without regard to
direction
• If you walk 7 km north of school this is
your position. If you walk back to the
school your position is zero even though
you walked 14 km. (7km away plus 7 km
back)
If there are turns, the
position might be different
from the distance traveled
Position vs time graph
• The position vs time
graph shows where an
object is at different
times
• Speed is the slope of
the position vs time
graph
Instantaneous and Average Speed
• Does your speed stay the same during a real trip?
– Of course not! You stop at lights, speed up to pass
• Average speed is how fast something moves over
a certain distance
– You travel 50 km in 2 hours
average speed = 25 km/hr
• Instantaneous speed is the speed of an object at a
specific point in its journey
Avg speed =
50 km =
2 hr
25 km/hr
Δd = df – di = 10km – 0km = 10km
Δt
tf – ti 0.5 hr – 0 hr 0.5 hr
Avg speed =
50 km =
2 hr
25 km/hr
Δd = df – di = 15km – 10km = 5 km
Δt
tf – ti 1 hr – 0.5 hr
0.5 hr
Avg speed =
50 km =
2 hr
25 km/hr
Δd = df – di = 30km – 15km = 15km
Δt
tf – ti 1.25 hr – 1 hr
.25 hr
Avg speed =
50 km =
2 hr
25 km/hr
Δd = df – di = 30km – 15km = 15km
Δt
tf – ti 1.25 hr – 1 hr
.25 hr
Speed vs. Velocity
• Speed is a description of how fast an object
moves
• Velocity is how fast an object moves and
the direction in which it moves; if either the
speed or the direction (or both) of an object
is changing, the velocity is changing.
• There are 3 controls in a car that can change
velocity. They are….?
Acceleration
• Acceleration is the rate of the change of
velocity
– Rate of change means the ratio of the amount of
change divided by how much time it took to
change
Acceleration = Change in velocity
Change in time (Δt)
Key idea for acceleration?
• Change – whenever we change our state of
motion, we are accelerating
• Acceleration applies to decreases
(deceleration or negative acceleration) and
increases in speed and any change in
direction
• When addressing only straight-line motion,
acceleration can be the rate at which speed
changes.
Units are cm/sec2
Types of Acceleration
• There are three different types of acceleration:
positive, negative, and zero acceleration
•Positive acceleration means the object is speeding up
•Negative acceleration means the object is slowing down
•Zero acceleration means the object is keeping the same speed
Calculating Acceleration
• Acceleration is the slope of the speed vs
time graph
• If a car speeds up, without changing direction,
from 0 to 10 km/h in 1 second, our
acceleration is
change in speed 10 km/h
Acceleration = time interval = 1s = 10 km/h-s
Two time entries in answer; first for unit of speed
(km/h), second for time interval in which speed is
changing (-s)
Practice problem #1
• A swimmer speeds up from 1.9 m/s to 2.6
m/s during the last 20 seconds of a workout.
What is the swimmer’s acceleration during
this time interval?
Practice problem #2
• In 5 seconds a car moving in a straight line
increases its speed from 50 km/h to 65 km/h,
while a truck goes from rest to 15 km/h in a
straight line.
– Which undergoes greater acceleration?
– What is the acceleration of each vehicle?
Practice problem #3
• Match each of the three distance vs time
graph with the corresponding speed vs time
graph.
Momentum
Momentum
• Momentum is the mass of an object
multiplied by its speed or velocity.
• If you increase the mass or the speed of an
object, you increase its momentum.
• Units are kg m/s
Mass (kg)
p  mv
Velocity (m/s)
Momentum (kgm/s)
The motion of objects
• If you throw a ball from your
skateboard, you must apply a force
to the ball.
• The 3rd law says the ball exerts a
force an equal and opposite force
on you.
• Your force makes the ball
accelerate in one direction and the
reaction makes you accelerate in
the opposite direction.
What happens if you throw a
heavier ball?
• If you throw the ball away very
fast, you backward acceleration is
higher than if you throw the ball
away slowly.
• If you throw a heavier ball away
fast, you backward acceleration is
greater than if you throw a lighter
ball.
• The backward acceleration is
called recoil.
Law of Conservation of
Momentum
• The law of the conservation of momentum
says that the total momentum of a system
can not change.
• That means that the momentum of the
system prior an action must equal the
momentum after the action.
• Positive and negative signs are used
to tell the direction of the motion.
That means momentum can be
positive (moving to the right) or
negative (moving to the left)
• Before you throw the ball, your and
the ball’s momentum is zero. In
order for conservation of momentum
to be true, after you throw the ball
the total momentum must be zero.
(1 kg)(-20 m/s) + (40kg)(0.5m/s) = 0
Homework 19
• Compare the momentums of a 65 kg dolphin
swimming 11.3 m/s and a 6500 kg elephant
walking 0.11 m/s.
Homework 23
•
A girl is riding her bike at a speed of 6 m/sec.
She then slows down to a speed of 2.5 m/sec.
The combined mass of the girl and bicycle is
50 kilograms.
a. What is her initial momentum?
b. What is her final momentum?
c. What is the change in momentum?