Physics 12 - Kinematics
Review
Speed vs. Velocity?
Rolling ball……..our first equation
Example
A car travels 60. km in 30. min, then turns
around and travels 30. in ½ hour.
What is the car’s speed over the entire trip? In
km/hr? In m/s?
What is the car’s average velocity in m/s over
the trip?
Acceleration
A change in velocity (speed or direction!!)
Rate of change of velocity (a=∆v/∆t)
2 important quantities to identify from a v-t
graph:
1. The slope of a line (gives us acceleration)
2. The area under a curve (gives us
displacement)
The other important equations…..
vf = vi + at
d = ½ (vf + vi)t
vf2 = vi2 + 2ad
d = vit + ½ at2
An object accelerates uniformly from rest. If the
final velocity of the object after 4.7 s is 15 m/s
east, what is it’s displacement?
Concept Questions…….
1. A person initially at point P in the illustration
stays there a moment and then moves along the
axis to Q and stays there a moment. She then
runs quickly to R, stays there a moment, and
then strolls slowly back to P. Which of the
position vs. time graphs below correctly
represents this motion?
2. An object goes from one point in space to another.
After it arrives at its destination, its displacement is:
a.
b.
c.
d.
e.
f.
either greater than or equal to
always greater than
always equal to
either smaller than or equal to
always smaller than
either smaller or larger
than the distance it traveled.
3. A marathon runner runs at a steady 15 km/hr. When
the runner is 7.5 km from the finish, a bird begins flying
from the runner to the finish at 30 km/hr. When the
bird reaches the finish line, it turns around and flies
back to the runner, and then turns around again,
repeating the back-and-forth trips until the runner
reaches the finish line. How many kilometers does the
bird travel?
a. 10 km
b. 15 km
c. 20 km
d. 30 km
4. A train car moves along a long straight track.
The graph shows the position as a function of
time for this train. The graph shows that the
train:
a. speeds up all the time.
b. slows down all the time.
c. speeds up part of the time and slows down
part of the time.
d. moves at a constant velocity
5. The graph shows position as a function of time
for two trains running on parallel tracks. Which is
true:
a. At time tB, both trains have the same velocity.
b. Both trains speed up all the time.
c. Both trains have the same velocity at some
time before tB.
d. Somewhere on the graph, both trains have the
same acceleration.
Free Fall
Gravity…..
g = +9.80 m/s2
or
g = -9.80 m/s2
You hold a ball in your hand at a fixed height and
release it. Its initial velocity is
a. up
b. zero
c. down
You hold a ball in your hand at a fixed height and
release it. Its initial acceleration is
a. up
b. zero
c. down
4. If you drop an object in the absence of air
resistance, it accelerates downward at 9.8 m/s2. If,
instead, you throw it downward, its downward
acceleration after release is
a. less than 9.8 m/s2.
b. 9.8 m/s2.
c. more than 9.8 m/s2.
You are throwing a ball straight up in the air. At the
highest point, the ball's
a.
b.
c.
d.
velocity and acceleration are zero
velocity is nonzero but its acceleration is zero
acceleration is nonzero, but its velocity is zero
velocity and acceleration are both nonzero
5. A person standing at the edge of a cliff throws
one ball straight up and another ball straight down
at the same initial speed. Neglecting air resistance,
the ball to hit the ground below the cliff with the
greater speed is the one initially thrown
a. upward
b. downward
c. neither-they both hit at the same speed
Example….
A rock is thrown with a velocity of 5.0 m/s
downward from a cliff of height 60. m.
How long does it take the rock to hit the
ground?
What is the rock’s speed when it hits the
ground?
Example
An object is launched directly upward with a
velocity of 7.9 m/s.
a. How long does it take to reach the top of the
trajectory?
b. What is the object’s velocity at t = 0.5 s? t = 3. s?
c. What is the object’s hang time ( total time in the
air)?
d. What is the max height reached?
Projectile Motion
Motion though the air without propulsion
Examples:
Part 1.
Motion of Objects Projected
Horizontally
y
v0
x
y
x
y
x
y
x
y
x
y
•Acceleration is constant (g = 9.80
m/s2 [downward] )
•vx is constant
•Horizontal and vertical motions are
independent of each other, but they
have a common time
g = -9.81m/s2
x
ANALYSIS OF MOTION
QUESTIONS:
•
What is the trajectory?
•
What is the total time of the motion?
•
What is the horizontal range?
•
What is the final velocity?
Question:
A ball is launched horizontally from the top of a
50.0 m tall cliff with a velocity of 20.0 m/s.
Find:
a)Flight time
b)Range
c) Final Velocity
Part 2.
Motion of objects projected at an
angle
What launch angle will produce the same range as….
a) 75o
b) 52o
c) 40o
y
• Acceleration is constant (g = 9.80 m/s2 [downward] )
• vx is constant
• Horizontal and vertical motions
are independent of each other, but
they have a common time
• Initial velocity must be broken
into it’s components!
x
Equations of motion:
X
Uniform motion
ax = 0
Y
Accelerated motion
ay = g = -9.81 m/s2
VELOCITY
vx = vi cos Θ
vy = vi sin Θ + g t
DISPLACEMENT
x = vi t cos Θ
y = vi t sin Θ + ½ g t2
ACCELERATION
Question:
A projectile is launched with a velocity of
100.0 m/s [35.0o N of E]
Find:
a)Time to the top
b)Maximum height
c)Total flight time
d)Range
e)What angle will produce the same range?
Answers….
a)
b)
c)
d)
e)
5.85 s
168 M
11.7 s
958 m
55o
Projectile Activity
Question:
A projectile is launched from the top of a 60.0
m building with a velocity of 50.0 m/s at an
angle of 30.0o with the horizontal.
Find:
a)Time to the top
b)Maximum height (relative to the ground)
c)Total flight time
d)Range
Relative Velocity
Always need a reference point
Example: VAB
Stated as: “Velocity of Object A relative
to Object B”
The Physics Classroom
Riverboats and Plane Problems
vresult = vboat + vwater
or
vresult = vplane + vwind
1. A plane can travel with a speed of
80. km/hr with respect to the air.
Determine the resultant speed (aka
‘ground speed’) of the plane if it
encounters a 21 km/hr cross wind.
2. A motorboat traveling 6 m/s East across a river
encounters a current traveling 3.8 m/s, South.
a. What is the resultant velocity of the motor boat?
b. If the width of the river is 120. meters wide, then how
much time does it take the boat to travel shore to
shore?
c. What distance downstream does the boat reach the
opposite shore?
3. An airplane flies west at 300. km/hr.
Wind blows North East at 100.
km/hr. What is the plane’s velocity
relative to the ground?
3. An airplane flies west at 300. km/hr.
Wind blows from the North East at
100. km/hr. What is the planes
velocity relative to the ground?
Remember:
vresult = vplane + vwind
Set up a table:
Vector
Plane
Wind
Result
X Component
Y-Component
Answers…
R = 239.9 km/hr [17o N of W]
The challenger….
4. A pilot wishes to fly to a city that is directly
752 km East of her position. Her air speed is
195 km/h and there is a wind from the north of
73 km/h.
a) What direction should she point the plane?
b) What will be her ground speed?
c) How long will it take to get there?
Answers…
a) Θ = 22o N of E
b) 195cos22o = 180.8 km/hr
c) t = 4.16 hr