AP Physics Part Mechanics by nikeborome


									A.   Kinematics in One Dimension
 Mechanics  – how &
  why objects move
 Kinematics: the
  description of how
  objects move
a.   Distance: total length of travel
b.   Displacement: change in position

Let’s say a runner jogs a lap around a 100-meter
   track. He returns back to where he started in
   4 minutes.
   a. What distance did he travel?
   b. What was his displacement?
 Our Very First Formula! Isn’t this exciting?
                   Δx = xf – xi ,

   Where Δx = change in position, or displacement,
                xf = final position, and
                   xi = initial position
*Displacement is directionally dependent! You CAN
  have negative displacement!
 Use   a visual!
 Does the odometer in your car measure
 distance or displacement?

    you think of a situation where it would
 Can
 measure both?
Aparticle moves from x = 1.0 m to x = -1.0 m.
 What is the distance? Displacement?
 Youare driving around a circular track with a
 diameter of 40 m. You drive around 2 ½ times.
 How far have you driven? What is your
Speed & Velocity
a.   Average Speed = distance traveled / elapsed
     time of travel
     Units: m/s

*Directionally Independent – always positive!
 Younose out another runner to win the
 100.000 m dash. If your total time for the race
 was 11.800 s and you aced out the other
 runner by 0.001 s, by how many meters did
 you win?
 Velocity:   speed AND direction
 Velocity= displacement/elapsed time
 Units: m/s

   Directionally DEPENDENT! Pick your frame of reference –
    which way is positive & which is negative?
   Your friend Marsha lives 0.55km east of your
    house. The nearest grocery store is 0.82km
    west of your house. You walk from your
    house to the grocery store for some soda. It
    takes you 17 minutes to get there, and you
    spend 3 minutes in the store. Then, in 12
    minutes, you walk from the grocery store
    over to Marsha’s house. Find the distance
    you traveled, your displacement, your
    average speed, and your average velocity.
 Graphposition vs. time for your trip to the
 grocery store & Marsha’s house.

 Theslope of the line along each interval shows
 your velocity!
Describe the object’s motion along each interval.
   Instantaneous velocity is an object’s speed at a
    point in time.
   On a position vs. time graph, it equals the slope
    of the tangent line at any time.
t(s)   x(m)
 0      0
0.25   9.85
0.50   17.2
0.75   22.3
1.00   25.6
1.25   27.4
1.50   28.1
1.75   28.0
2.00   27.4
    Review: v=Δd/Δt
a.    Acceleration: how quickly an object’s velocity
b.    Acceleration can be:
     a. Speeding up (v and a are in same direction)
     b. Slowing down (different sign for v and a)
     c. Changing direction (2-D motion)
 Units    for acceleration are m/s2

   In Physics B, we assume acceleration is constant.
 Saab advertises a car that goes from 0 to 60.0
 mi/h in 6.2s. What is the average acceleration
 of this car?

 Anairplane has an average acceleration of 5.6
 m/s2 during takeoff. How long does it take for
 the plane to reach a speed of 150 mi/h?
   Instantaneous acceleration can be found by
    calculating the slope of the tangent line at a
    point on a velocity vs. time graph.
   Constant acceleration (in an ideal world):
    instantaneous a = average a
Kinematic Equations
   A car slows down along the road from 40.0
    km/h to 24.0 km/h in just 3.70 seconds.
    What is the car’s acceleration?

   A ball is thrown into the air at a velocity of
    15.0 m/s. It is caught at the same height
    when it is traveling downward at a speed of
    15.0 m/s. Find the average velocity of the
A  ball is dropped (not thrown) from a height of
  77.2m. How long does it take to hit the
  ground below? (neglect air resistance and
  remember gravitational acceleration=
 A skydiver is falling at a velocity of 8.2 m/s
  downward. The parachute is opened, and
  after falling 19m, the skydiver is falling at a
  rate of 2.7m/s. What deceleration did the
  parachute provide?
1. A child slides down a hill on a sled with an
  acceleration of 1.5 m/s2. If she starts at rest,
  how far has she traveled in (a) 1.0s, (b) 2.0s,
  and (c) 3.0s?
2. On a ride at an
  amusement park,
  passengers accelerate
  straight downward from
  zero to 45mi/h in 2.2s.
  What is the average
  acceleration of
  passengers on this ride?
4. Two cars drive on a straight highway. At time t=0,
  car 1 passes mile marker 0 traveling due east with a
  speed of 20.0 m/s. At the same time, car 2 is 1.0 km
  east of mile marker 0 traveling at 30.0 m/s due west.
  Car 1 is speeding up with an acceleration of
  magnitude 2.5 m/s2, and car 2 is slowing down with
  an acceleration of magnitude 3.2 m/s2. Write x-
  versus-t equations of motion for both cars.
5. You’re driving around town at 12.0 m/s when
  a kid runs out in front of your car. You brake –
  your car decelerates at 3.5 m/s/s.
(a) How far do you travel before stopping?
(b) When you have traveled half that distance,
    what is your speed?
(c) How much time does it take to stop?
(d) After braking half that time, what is your
a. Objects of different masses/weights fall with
   (at sea level & neglecting air resistance)
b. What acts on an object in free fall?
   -NOTHING but gravity (hence the free)
c. Objects in free fall can move down, OR up!

d. g = 9.81 m/s/s ← g is always positive 9.81
  m/s/s. If your frame of reference says
  down is negative, use –g.
*If down is positive and x0=0, then x=1/2 gt2
(derived from that super-important eqn)
 At what acceleration
  does a 5000kg elephant
 What about a mouse?
 You   drop a ball from a 120-m high cliff
  • How long is it in the air?

  • What is its speed just before it hits the ground? (at

  • Sketch x vs t, v vs t, and a vs t graphs for this
ketch x vs t, v vs t, and a vs t graphs for this

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