QotD • Draw a model of the following situation • A cyclist on a world tour bikes due north for 20 km when he sees a Shell gas station and thinks about getting some water for his trip. But he decides that he will wait until the next station comes up. After another 20 km, he realizes that there are no convenient stores for 30 more km, so he decides to bike back to the Shell station to get water and rest. • What is the cyclist’s total distance traveled? • What is the cyclist’s total displacement?
Transcript
QotD• Draw a model of the following situation• A cyclist on a world tour bikes due north for 20 km when he sees a
Shell gas station and thinks about getting some water for his trip. But he decides that he will wait until the next station comes up. After another 20 km, he realizes that there are no convenient stores for 30 more km, so he decides to bike back to the Shell station to get water and rest.
• What is the cyclist’s total distance traveled?
• What is the cyclist’s total displacement?
2-1 Reference Frames and Displacement
We make a distinction between distance and displacement.
Displacement (blue line) is how far the object is from its starting point, regardless of how it got there.
Distance traveled (dashed line) is measured along the actual path.
2-1 Reference Frames and Displacement
The displacement is written:
Right:
Displacement is positive.
Left:
Displacement is negative.
You and your dog go for a walk to the You and your dog go for a walk to the
park. On the way, your dog takes many park. On the way, your dog takes many
side trips to chase squirrels or examine side trips to chase squirrels or examine
fire hydrants. When you arrive at the fire hydrants. When you arrive at the
park, do you and your dog have the same park, do you and your dog have the same
displacement?displacement?
1) yes
2) no
ConcepTest 2.1ConcepTest 2.1 Walking the DogWalking the Dog
You and your dog go for a walk to the You and your dog go for a walk to the
park. On the way, your dog takes many park. On the way, your dog takes many
side trips to chase squirrels or examine side trips to chase squirrels or examine
fire hydrants. When you arrive at the fire hydrants. When you arrive at the
park, do you and your dog have the same park, do you and your dog have the same
displacement?displacement?
1) yes
2) no
Yes, you have the same displacement. Since you and your dog had
the same initial position and the same final position, then you have (by
definition) the same displacement.
ConcepTest 2.1ConcepTest 2.1 Walking the DogWalking the Dog
Follow-up:Follow-up: Have you and your dog traveled the same distance? Have you and your dog traveled the same distance?
Graphing• What is the displacement from t1 = 0 s to t2 = 9 s?
• What is the distance traveled during this time?
2-2 Average Velocity
Speed: how far an object travels in a given time interval
Velocity includes directional information:
(2-1)
If the position of a car is If the position of a car is
zero, does its speed have zero, does its speed have
to be zero?to be zero?
1) yes
2) no
3) it depends on the
position
ConcepTest 2.3ConcepTest 2.3 Position and SpeedPosition and Speed
If the position of a car is If the position of a car is
zero, does its speed have zero, does its speed have
to be zero?to be zero?
1) yes
2) no
3) it depends on the
position
No, the speed does not depend on position, it depends on the change
of position. Since we know that the displacement does not depend on
the origin of the coordinate system, an object can easily start at x = –3
and be moving by the time it gets to x = 0.
ConcepTest 2.3ConcepTest 2.3 Position and SpeedPosition and Speed
You drive 4 miles at 30 mi/hr and
then another 4 miles at 50 mi/hr.
What is your average speed for
the whole 8-mile trip?
1) more than 40 mi/hr
2) equal to 40 mi/hr
3) less than 40 mi/hr
ConcepTest 2.4 ConcepTest 2.4 Cruising Along IICruising Along II
You drive 4 miles at 30 mi/hr and
then another 4 miles at 50 mi/hr.
What is your average speed for
the whole 8-mile trip?
1) more than 40 mi/hr
2) equal to 40 mi/hr
3) less than 40 mi/hr
It is not 40 mi/hr! Remember that the average speed is distance/time.
Since it takes longer to cover 4 miles at the slower speed, you are
actually moving at 30 mi/hr for a longer period of time! Therefore,
your average speed is closer to 30 mi/hr than it is to 50 mi/hr.
ConcepTest 2.4 ConcepTest 2.4 Cruising Along IICruising Along II
2-3 Instantaneous Velocity
These graphs show (a) constant velocity and (b) varying velocity.
Po
siti
on
(m
)Using graphs to determine velocity
01020
30405060
708090
10 30 50 70 90 110
130
150
Time (s)
avg
xv slope
t
(60m-20m)/(35s-15s)=2m/s
negative velocity
(90m-50m)/(110s-85s)=0.004m/s
ConcepTest 2.7 Velocity in One Dimension
If the If the averageaverage velocity is non-zero over some velocity is non-zero over some
time interval, does this mean that the time interval, does this mean that the
instantaneousinstantaneous velocity is velocity is nevernever zero during zero during
the same interval?the same interval?
1) yes
2) no
3) it depends
ConcepTest 2.7 Velocity in One Dimension
No!!! For example, your average velocity for a trip home
might be 60 mph, but if you stopped for lunch on the way
home, there was an interval when your instantaneous
velocity was zero, in fact!
1) yes
2) no
3) it depends
If the If the averageaverage velocity is non-zero over some velocity is non-zero over some
time interval, does this mean that the time interval, does this mean that the
instantaneousinstantaneous velocity is velocity is nevernever zero during zero during
the same interval?the same interval?
• Your turn:• If you are driving 110 km/hr along a straight road and you look
to the side for 2.0 s, how far do you travel during this inattentive period?
• What is that in miles? (1 km = 0.62 mi)
Qotd: How do we graph velocity vs time?• Calculate slope for given time intervals• Plot velocity vs time
Motion Graphs• Draw the position vs time (x vs t) and velocity vs time (v vs t)
graphs for the following situation:
• A student walking toward their locker at a constant speed and then suddenly realizing they had left something in their classroom and turning around to walk away from their locker at a faster rate
2-4 AccelerationAcceleration is the rate of change of velocity.
2-4 Acceleration
Acceleration is a vector, although in one-dimensional motion we only need the sign.
The previous image shows positive acceleration; here is negative acceleration:
ConcepTest 2.8a Acceleration I
If the velocity of a car is non-zero If the velocity of a car is non-zero
((v v 00), can the acceleration of the ), can the acceleration of the
car be zero?car be zero?
1) yes
2) no
3) depends on the
velocity
ConcepTest 2.8a Acceleration I
If the velocity of a car is non-zero If the velocity of a car is non-zero
((v v 00), can the acceleration of the ), can the acceleration of the
car be zero?car be zero?
Sure it can! An object moving with constantconstant velocityvelocity
has a non-zero velocity, but it has zerozero accelerationacceleration
since the velocity is not changing.
1) yes
2) no
3) depends on the
velocity
Your turn:• A sports car accelerates from rest to 95 km/hr in 6.2 s. What is
its average acceleration in m/s2?
QotD
What’s the difference between negative acceleration and deceleration?
2-4 Acceleration
There is a difference between negative acceleration and deceleration:
Negative acceleration is acceleration in the negative direction as defined by the coordinate system.
Deceleration occurs when the acceleration is opposite in direction to the velocity.
The Big Three
The Big Three
Question of the Day• How much time does Mr. Deer have to cross the street without
getting hit?
Question of the Day• How much time does Mr. Deer have to cross the street without
getting hit?
• Car velocity in picture: 15 m/s• Accelerating at 2 m/s2
• Displacement = 45 m• You don’t see the deer
2-7 Falling Objects
Near the surface of the Earth, all objects experience approximately the same acceleration due to gravity.
This is one of the most common examples of motion with constant acceleration.
2-7 Falling Objects
The acceleration due to gravity at the Earth’s surface is approximately 9.80 m/s2.
When throwing a ball straight up, When throwing a ball straight up,
which of the following is true about which of the following is true about
its velocity its velocity vv and its acceleration and its acceleration aa
at the highest point in its path?at the highest point in its path?
1) both 1) both v = 0v = 0 and and a = 0a = 0
2) 2) v v 0 0, but , but a = 0a = 0
3) 3) v = 0v = 0, but , but a a 0 0
4) both 4) both v v 00 and and a a 0 0
5) not really sure5) not really sure
ConcepTest 2.8bConcepTest 2.8b Acceleration IIAcceleration II
y
At the top, clearly v = 0 because the ball has
momentarily stopped. But the velocity of the
ball is changing, so its acceleration is definitely
not zero! Otherwise it would remain at rest!!
When throwing a ball straight up, When throwing a ball straight up,
which of the following is true about which of the following is true about
its velocity its velocity vv and its acceleration and its acceleration aa
at the highest point in its path?at the highest point in its path?
1) both 1) both v = 0v = 0 and and a = 0a = 0
2) 2) v v 0 0, but , but a = 0a = 0
3) 3) v = 0v = 0, but , but a a 0 0
4) both 4) both v v 00 and and a a 0 0
5) not really sure5) not really sure
ConcepTest 2.8bConcepTest 2.8b Acceleration IIAcceleration II
Follow-up:Follow-up: …and the value of …and the value of aa is…? is…?
2-8 Graphical Analysis of Linear Motion
The displacement, x, is the area beneath the v vs. t curve.
• QotD• From memory, write out the BIG 3 equations for constant
acceleration motion
• Free Fall Practice:• How long does it take King Kong to fall straight down from the
top of the Empire State Building (380 m high)?• What is his velocity just before landing?
• Practice Question (WA Help)• In coming to a stop, a car leaves skid marks 92 m long on the
highway. Assuming a deceleration of 7.00 m/s2 estimate the speed of the car just before braking. (P 2.26)
QotD:An aircraft needs to be going at a speed of 33 m/s to lift off the ground. The acceleration provided by the engines is 3.5 m/s2. How long does the runway need to be so the plane can take off?
Your turn:A world-class sprinter can burst out of the blocks to essentially top speed (of about 11.5 m/s) in the first 15.0 m of the race. What is the average acceleration of this sprinter, and how long does it take her to reach that speed?
