Physics 2211a Kulp Class 5: What is the effect of acceleration

1
Physics 2211a (Kulp)Class 5 What is the
effect of acceleration?
If your name does not appear with your PRS, see
me! Class TA Mauricio Bedoya W,Th 2-4
PM Recitation TA Ekapop Pairam

• W. D. Kulp
• william.kulp at physics.gatech.edu
• Office W501b
• Office Hours MF 11-12 AM, Tu 9-10 AM, by appt.
• www.physics.gatech.edu/academics/Classes/fall200
  6/2211/a/

2
Where were we?

• Last Meeting Class 4
• Translate verbal, pictorial and physical
  representations of position and velocity into a
  graphical representation.
• Interpret a graph of either position or velocity
  as a function of time to determine in what time
  intervals the values are positive, negative, or
  zero, and draw a graph of the other quantity as a
  function of time.

3
Instantaneous velocity
The position of a particle as a function of time
is given by Where c is a positive constant.
Find the instantaneous velocity as a function
of time.

• From calculus, we know the form of a derivative
  of a power or polynomial function

• If we have a function of two variables (e.g., x
  and y as well see later)

4
Trucker Bob

• Trucker Bob starts the day 120 miles west of
  Denver. He drives east for 3 hours at a steady
  60 mph before stopping for his coffee break. Let
  Denver be located at x0 and assume that the
  x-axis points to the east.

• How far has Bob traveled at t1 h? At t2 h and
  t3 h?
• t 1 h 60 mi
• t 2 h 120 mi
• t 3 h 180 mi
• 60 miles for each hour traveled

5
Trucker Bob

• Trucker Bob starts the day 120 miles west of
  Denver. He drives east for 3 hours at a steady
  60 mph before stopping for his coffee break. Let
  Denver be located at x0 and assume that the
  x-axis points to the east.

• Sketch the position-versus-time graph for Bob.

6
Where are we?

• Last Meeting Class 4
• Translate verbal, pictorial and physical
  representations of position and velocity into a
  graphical representation.
• Interpret a graph of either position or velocity
  as a function of time to determine in what time
  intervals the values are positive, negative, or
  zero, and draw a graph of the other quantity as a
  function of time.

• Today Class 5
• Using a graph of position, velocity, or
  acceleration as a function of time, determine in
  what time intervals the other two quantities are
  positive, negative, or zero and draw a graph of
  each value as a function of time.

7
Changing velocity
v (m/s)
40
10 m/s2
30

• A car has the velocity shown in the graph on the
  right. Consider the questions below

20
10
t (s)

• What is the displacement of the car at time t1?
  At t2, t4?
• What is the acceleration of the car?
• Write an algebraic statement describing the
  displacement of the car as a function of
  velocity.
• Write an algebraic statement describing the
  displacement of the car as a function of
  acceleration.

1
2
3
4
8
Changing velocity
v (m/s)
40
10 m/s2
30

• A car has the velocity shown in the graph on the
  right. Consider the questions below

20
10
t (s)

• What is the displacement of the car at time t1?
  At t2, t4?
• What is the acceleration of the car?
• Write an algebraic statement describing the
  displacement of the car as a function of velocity
  for t1 to t3.
• Write an algebraic statement describing the
  displacement of the car as a function of
  acceleration.

1
2
3
4
9
Walking exercise accelerating
v (m/s)

• Dr. Kulp starts walking from rest from left to
  right, speeding up while moving, and passes the
  origin at top speed.

t (s)
X0 lt 0 v0 0 t0 0
X1 0 v1 v t1 t1
Xf gt 0 vf v tf tf
t1
tf
x (m)
0

• Sketch pictorial representation
• Draw motion diagram
• Plot x vs. t
• Plot vx vs. t
• Plot ax vs. t

t (s)
t1
tf
10
Walking exercise accelerating
v (m/s)

• Dr. Kulp starts walking from rest from left to
  right, speeding up while moving, and passes the
  origin at top speed.

t (s)
X0 lt 0 v0 0 t0 0
X1 0 v1 v t1 t1
Xf gt 0 vf v tf tf
t1
tf
a (m/s2)
0

• Sketch pictorial representation
• Draw motion diagram
• Plot x vs. t
• Plot vx vs. t
• Plot ax vs. t

t (s)
t1
tf
11
Cart on a track 1
x (m)
x
V00
X00

• A cart is released from rest as illustrated
  above. Plot graphs of position, velocity, and
  acceleration as functions of time.

t (s)
a (m/s2)
v (m/s)
t (s)
t (s)
12
Cart on a track 2
x (m)
x

• A cart is pushed up the ramp. Plot graphs of
  position, velocity, and acceleration as functions
  of time.

t (s)
v (m/s)
a (m/s2)
t (s)
t (s)
13
Cart on a track 3
x (m)
x
V0lt0
X0gt0

• A cart is pushed up the ramp and rolls back down
  to its starting position.
• Plot graphs of position, velocity, and
  acceleration as functions of time.

t (s)
v (m/s)
a (m/s2)
t (s)
t (s)
14
Whats next?

• Friday, 9/1 Class 6 How does the Earth affect
  motion?
• Recognize free fall and describe the situation
  algebraically using g, the acceleration due to
  gravity.
• Identify physical situations which exhibit
  uniformly accelerated motion, write equations
  describing the motion, and solve for unknown
  observables.

• To-do list
• Find lab recitation rooms
• Find N209 (Help Lab)
• Homework 5 before next class
• Read assignment (2.6-2.7)

15
Lab notes

• Constant acceleration

• What is the time required to travel distance d?