Physics 100

1
Physics 100

• Sections A1, A2, A3 and A4

2
Physics 100

• Chapter 2 (Section 4)

Motion with constant Acceleration
3
Constant Acceleration
a
For a particle moving with constant acceleration
velocity changes at the same rate throughout the
motion.
v
t 0
x
0
a
v
t ?t
x
0
a
v
t 2?t
x
0
a
v
t 3?t
x
0
a
v
t 4?t
x
0
4
Constant Acceleration
ax-t graph
ax
ax
t
t
O
5
Constant Acceleration
ax-t graph
ax
same acceleration all the time
ax
t
t
O
6
Constant Acceleration
ax-t graph
ax
same value of acceleration all the time
ax
t
t
O
7
Constant Acceleration
vx-t graph
vx
t
O
8
Constant Acceleration
vx-t graph
vx
same slope all the time ax
t
O
9
Constant Acceleration
vx-t graph
vx
same slope all the time ax
vx
axt
vx
v0x
v0x
t
O
t
10
Constant Acceleration
Constant acceleration
11
Constant Acceleration
Constant acceleration
at t 0, v v0x,
12
Constant Acceleration
Constant acceleration
at t 0, v v0x,
Constant acceleration only
13
Constant Acceleration
Constant acceleration
14
Constant Acceleration
Constant acceleration
15
Constant Acceleration
Constant acceleration
16
Constant Acceleration
Constant acceleration
Constant acceleration only
17
Constant Acceleration
x-t graph
x
x
x0
t
O
t
18
Constant Acceleration
x-t graph
x
Slope vx
x
Slope v0x
x0
t
O
t
19
Constant Acceleration
Constant acceleration only
Constant acceleration only
Constant acceleration only
20
Constant Acceleration ONLY
Missing Quantity
Equation
21
Motion with Constant Acceleration
Problem-Solving Strategy

• IDENTIFY the relevant concepts
• In most straight-line motion problems, you can
  use the constant-acceleration equations.
• SET UP the problem
• Decide about the origin and direction of the
  axes. Draw the diagram. List quantities like
  x0,v0, vx, etc and decide which quantity is
  missing.
• EXECUTE the solution
• Choose an equation that contains only one of the
  target variables.
• EVALUATE your answer
• Does it make sense.

22
Constant Acceleration
Example 2.4

• A motorcyclist heading east through a small city
  accelerates after he passes a signpost. His
  acceleration is a constant 4.0 m/s2. At time t0
  he is 5.0 m east of the signpost, moving east at
  15 m/s.
• (a) Find his position and velocity at time t2.0
  s.
• (b) Where is the motorcyclist when his velocity
  is 25 m/s.

23
Constant Acceleration
Example 2.4

• IDENTIFY The problem states that the
  acceleration is constant.

24
Constant Acceleration
Example 2.4

• IDENTIFY The problem states that the
  acceleration is constant.
• SET UP Take the signpost as the origin (x0),
  and choose v x-axis to be east.

25
Constant Acceleration
Example 2.4

• IDENTIFY The problem states that the
  acceleration is constant.
• SET UP Take the signpost as the origin (x0),
  and choose v x-axis to be east.
• At t 0, x0 5.0 m, v0x 15 m/s
• constant acceleration ax4.0 m/s2
• target variables (a) x and vx at t 2.0 s
• (b) x when vx 25 m/s

26
Constant Acceleration
Example 2.4

• EXECUTE (a)

27
Constant Acceleration
Example 2.4

• EXECUTE (a)

28
Constant Acceleration
Example 2.4

• EXECUTE (a)

29
Constant Acceleration
Example 2.4

• EXECUTE (a)
• x x0 v0xt (1/2) axt2
• x 5.0 m (15 m/s)(2.s) (1/2)(4.0 m/s2)(2.0
  s)2
• 43 m

30
Constant Acceleration
Example 2.4

• EXECUTE (a)

31
Constant Acceleration
Example 2.4

• EXECUTE (a)

32
Constant Acceleration
Example 2.4

• EXECUTE (a)
• x x0 v0xt (1/2) axt2
• x 5.0 m (15 m/s)(2.s) (1/2)(4.0 m/s2)(2.0
  s)2
• 43 m
• vx v0x axt
• 15 m/s (4.0 m/s2)(2.0 s) 23 m/s

33
Constant Acceleration
Example 2.4

• EXECUTE (b)

34
Constant Acceleration
Example 2.4

• EXECUTE (b)
• vx2 - v0x2 2 ax(x - x0)
• (25 m/s)-(15 m/s) 2 (4.0 m/s2) (x 5.0 m)
• ? x 55 m
• EVALUATE

35
Check Point
vx
a
b
d
c
t
O
36
Check Point
Which curves represent Constant velocity?
vx
a
b
d
c
t
O
37
Check Point
Which curves represent Constant velocity?
vx
a
a
b
d
c
t
O
38
Check Point
Which curves represent Constant acceleration?
vx
a
b
d
c
t
O
39
Check Point
Which curves represent Constant acceleration?
vx
a
c
b
a
b
d
c
t
O
40
Check Point
Which curves represent Initial velocity not
zero?
vx
a
b
d
c
t
O
41
Check Point
Which curves represent Initial velocity not
zero?
vx
a
b
d
b
a
c
t
O
42
Check Point
Which curves represent Constant
velocity? Constant acceleration? Initial velocity
not zero?
vx
a
a
c
b
a
b
d
b
a
c
t
O
43
Constant Acceleration
Example 2.5

• A Car traveling with constant velocity of 15 m/s
  (where speed limit is 10 m/s) passes a parked
  police car. The officer starts of in pursuit with
  constant acceleration of 3.0 m/s2.
• (a) How much time elapse before the officer
  catches up with the car?
• (b) What is the officers speed at that point?
• (c) What is the total distance each vehicle
  traveled at that point?

44
Constant Acceleration
Example 2.5
x (m)

• A Car traveling with constant velocity of 15 m/s
  (where speed limit is 10 m/s) passes a parked
  police car. The officer starts of in pursuit with
  constant acceleration of 3.0 m/s2.

160
120
80
40
t (s)
O
2
4
6
8
10
12
45
Constant Acceleration
Example 2.5
x (m)

• A Car traveling with constant velocity of 15 m/s
  (where speed limit is 10 m/s) passes a parked
  police car. The officer starts of in pursuit with
  constant acceleration of 3.0 m/s2.

160
120
80
40
t (s)
O
2
4
6
8
10
12
46
Constant Acceleration
Example 2.5
x (m)

• A Car traveling with constant velocity of 15 m/s
  (where speed limit is 10 m/s) passes a parked
  police car. The officer starts of in pursuit with
  constant acceleration of 3.0 m/s2.

160
120
80
40
t (s)
O
2
4
6
8
10
12
47
Constant Acceleration
Example 2.5
x (m)

• A Car traveling with constant velocity of 15 m/s
  (where speed limit is 10 m/s) passes a parked
  police car. The officer starts of in pursuit with
  constant acceleration of 3.0 m/s2.

160
120
80
40
t (s)
O
2
4
6
8
10
12
48
Constant Acceleration
Example 2.5

• IDENTIFY The problem states that the
  accelerations are constant (car 0 m/s2, police
  axp 3.0 m/s2)
• SET UP
• Take the origin at the passing point.
• Positive direction to the right.
• Take xm motorist position, xp police position.
• At the catching point xm xp

49
Constant Acceleration
Example 2.5

• EXECUTE (a)
• xm xm0vm0xt0.5am0xt2 0vm0xt0.5(0)t2
• vm0x t
• xp xp0vp0xt0.5ap0xt2 0(0)t0.5ap0xt2
• 0.5 ap0x t2
• At the catching point
• xm xp
• vm0x t 0.5 ap0x t2 ? t 10 s

50
Constant Acceleration
Example 2.5

• EXECUTE (b)
• vpx vp0x apxt
• 0 (3.0 m/s2) (10 s)
• 30 m/s

51
Constant Acceleration
Example 2.5

• EXECUTE (b)
• vpx vp0x apxt
• 0 (3.0 m/s2) (10 s)
• 30 m/s
• (c)
• xm vm0xt
• (15 m/s) (10 s)
• 150 m

52
Constant Acceleration
Example 2.5

• EXECUTE (b)
• vpx vp0x apxt
• 0 (3.0 m/s2) (10 s)
• 30 m/s
• (c)
• xm vm0xt xp 0.5 ap0x t2
• (15 m/s) (10 s) 0.5(3.0m/s2)(10 s)2
• 150 m 150 m

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And the lessons continue