25
Martha Casquete
Martha Casquete
Would you risk your live driving drunk?
Intro
Acceleration
Constant acceleration: A special case
Free fall acceleration
Motion
Position and displacement
Average velocity and average speed
Instantaneous velocity and speed
Assignments: For next class: Read Chapter 3 (Vectors)
HW3 Set due next Tuesday, 9/10 Pg. 48 – 52: 5, 11, 18, 40, 49 (8th edition)
Question/Observation Thursdays Research Q/O Tuesdays with HW (due date
Tuesdays)
A cheetah is crouched in ambush 20 m to the east of an observer’s blind. At time t= 0 the cheetah charges an antelope in a clearing 50 m east of the observer. The cheetah runs along a straight line. Later analysis of a videotape shows that during the first 2.0 s of the attack, the cheetah’s coordinator x varies with time according to the equation x = 20m + (5.0m/s2 )t2 a) Find the displacement of the cheetah during the interval between t1 = 1.0 s and t2 = 2.0 s
b) Find the average velocity during the same time interval. c) Find the average velocity at time t1 = 1.0 s by taking ∆t = 0.1 s. d) Derive a general expression for the instantaneous velocity as a function of time, and from it find v at t = 1.0 s and = 2.0 s.
Uniform velocity is constant velocity
The instantaneous velocities are always the same, all the instantaneous velocities will also equal the average velocity
Begin with then
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Changing velocity (non-uniform) means an acceleration is present.
Acceleration is the rate of change of velocity.
Acceleration is a vector quantity.
Acceleration has both magnitude and direction.
Acceleration has a unit of [length/time2]: m/s2.
Definition: ◦ Average acceleration
◦ Instantaneous acceleration if
if
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Average acceleration
Velocity as a function of time
When the sign of the velocity and the acceleration are the same (either positive or negative), then the speed is increasing
When the sign of the velocity and the acceleration are in the opposite directions, the speed is decreasing
Average acceleration is the slope of the line connecting the initial and final velocities on a velocity-time graph
if
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The limit of the average acceleration as the time interval goes to zero
When the instantaneous accelerations are always the same, the acceleration will be uniform. The instantaneous acceleration will be equal to the average acceleration
September 8, 2008
Velocity and acceleration are in the same direction
Acceleration is uniform (blue arrows maintain the same length)
Velocity is increasing (red arrows are getting longer)
Positive velocity and positive acceleration
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Position is a function of time:
Velocity is the rate of change of position.
Acceleration is the rate of change of velocity.
Position Velocity Acceleration
Graphical relationship between x, v, and a
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Uniform acceleration is constant
Kinematic Equations
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Given initial conditions: ◦ a(t) = constant = a, v(t=0) = v0, x(t=0) = x0
Start with
We have
Shows velocity as a function of acceleration and
time Use when you don’t know and aren’t asked to
find the displacement
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Given initial conditions:
◦ a(t) = constant = a, v(t=0) = v0, x(t=0) = x0
Start with
Since velocity change at a constant rate, we have
Gives displacement as a function of velocity and time
Use when you don’t know and aren’t asked for the acceleration
t
x
t
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10
Given initial conditions: ◦ a(t) = constant = a, v(t=0) = v0, x(t=0) = x0
Start with
We have
Gives displacement as a function of time, initial velocity and acceleration
Use when you don’t know and aren’t asked to find the final velocity
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Given initial conditions: ◦ a(t) = constant = a, v(t=0) = v0, x(t=0) = x0
Start with
We have
Gives velocity as a function of acceleration and
displacement Use when you don’t know and aren’t asked for the
time
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Read the problem Draw a diagram ◦ Choose a coordinate system, label initial and final
points, indicate a positive direction for velocities and accelerations
Label all quantities, be sure all the units are consistent ◦ Convert if necessary
Choose the appropriate kinematic equation Solve for the unknowns ◦ You may have to solve two equations for two
unknowns
Check your results ◦ Estimate and compare ◦ Check units
An electron in a cathode-ray tube accelerates from a speed of 2.00 X 10 m/s over 1.50 cm. (a) in what time interval does the electron travel this 1.50 cm? (b) What is the acceleration
Earth gravity provides a constant acceleration. Most important case of constant acceleration.
Free-fall acceleration is independent of mass.
Magnitude: |a| = g = 9.8 m/s2
Direction: always downward, so ag is negative if define “up” as positive,
a = -g = -9.8 m/s2
Try to pick origin so that xi = 0
y
Galileo Galilei (1564 - 1642
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Two important equation:
Begin with t0 = 0, v0 = 0, x0 = 0
So, t2 = 2|x|/g same for two balls!
Assuming the leaning tower of Pisa is 150 ft high, neglecting air resistance,
t = (21500.305/9.8)1/2 = 3.05 s
x
0
A student throws a set of keys vertically upward to her sorority sister, who is in a window 4.00m above. The key are caught 1.50 s later by the sister’s outstretched hand. (a) With what initial velocity were the keys thrown? (b) What was the velocity of the keys just before they were caught?
2-23
If frictional effects (air resistance) are neglected, every freely falling object on earth accelerates at the same rate, regardless of mass. Galileo is credited with this idea/experiment.
Astronaut David Scott demonstrated the principle on the moon, simultaneously dropping a feather and a hammer. Each fell at the same acceleration, due to no atmosphere & no air resistance.
Section 2.3 http://www.youtube.com/watch?v=KDp1tiUsZw8
What do you need?
Ruler
Pencil
Paper
Brain
Volunteer with two fingers
This is the simplest type of motion It lays the groundwork for more complex motion Kinematic variables in one dimension
◦ Position x(t) m L ◦ Velocity v(t) m/s L/T ◦ Acceleration a(t) m/s2 L/T2 ◦ All depend on time ◦ All are vectors: magnitude and direction vector:
Equations for motion with constant acceleration: missing quantities ◦ x – x0
◦ v
◦ t
◦ a ◦ v0
2
21
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0
September 8, 2008
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