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ACCELERATIONzoom zoom
ACCELERATION TERMS
Acceleration (a)– the rate of change of velocity (can be +, -, or centripetal)
Deceleration– only negative acceleration (slowing down)
Centripetal Acceleration– acceleration that occurs when changing direction (turning)
Freefall– objects falling due to gravity Force is what you feel when you
accelerate
3 WAYS TO ACCELERATE
Since acceleration is a change in velocity and velocity has 2 parts
We can accelerate by Changes in speed
1. Speed up (+ acceleration)2. Slow down (- acceleration)
Changing Direction3. Turning
Changing both speed and direction
YOUR SPEEDOMETER – THE KEY TO ACCEL We don’t see
acceleration of an object well with our eyes
But if we look at a speedometer we can see speed change.
Acceleration is a picture of what your speedometer is doing
ACCELERATION IS A PIC OF YOUR SPEEDO
SLOW ACCELERATION FAST(ER) ACCELERATION
THE ACCELERATION GRAPH SETUP
THE VARIABLES THE GRAPH
Speed ( or velocity)is the dependent variable
Time is the independent variable
Time
Spee
d
Graph setup = Formula
a=DspDt
ACCELERATION& SLOPE (QUICK VERSION) Acceleration(Dsp/Dt)= slope on an acceleration graph (rise/run)
Acceleration Graph
Time
Spee
d
+ acceleration (gas pedal)
Constant Speed(0 acceleration)(cruise control)
- Acceleration (deceleration)(brake pedal)
No motion - stopped
ACCELERATION GRAPHS & SLOPE & SPEED
• Positive (+) slope = + accel (speeding up)
• Negative (-) slope = - accel (slowing down)
• Zero (0) slope (flat line) = 0 accel (constant speed)
spee
d
t
tsp
eed
tsp
eed
SLOPE & TYPE OF ACCELERATION
• Steeper slopes show greater acceleration• Straight lines = Constant acceleration• Steady increase or decrease in speed
spee
d
tsp
eed
t
Accelerates quickly
Accelerates slowly
decelerates slowly
decelerates quickly
When is the speed = to 0 (stopped)?
DISCUSS THIS GRAPH
Describe which sport you think this graph represents and why. Golf Skydiving Fishing 100-meter dash Drag racing
Speed
Time
CALCULATING ACCELERATION FROM SLOPE Rise–change in the graph on the vertical axis (Speed) Run–change in the graph on the horizontal axis (Time)
Acceleration=sp2-sp1
t2-t1Slope = =
Y2-y1
X2-x1
riserun
0 10 20 30 40 50 60 700
5
10
15
20
25
Acceleration (km/h/s)
Time (s)
sp
eed
(km
/h)
P1 (0 s, 0 km/h) t1 sp1
P2 (20 s, 20 km/h) t2 sp2
P1
P2
a=sp2-sp1
t2-t1
=
20 km/h
20 s=
= 1 km/h/s
20 km/h - 0 km/h
20 s– 0 s
ANSWERS TO SAMPLE QUESTIONS
What is the acceleration of the object from 0 – 20 s?
What is the speed of the object from 20 – 40 s?
What is the speed of the object from 40 – 60 s?
Acceleration(slope) =
sp2 – sp 1
(rise)t2 – t1 (run)
=(20–0 m/s)( 20 – 0 s)
=20 m/s20 s
= 1 m/s/s
Acceleration(slope) =
sp2 – sp 1
(rise)t2 – t1 (run)
=(20–20 m/s)( 40 – 20 s)
=0 m/s
20 s
= 0 m/s/s
Acceleration(slope) =
sp2 – sp 1
(rise)t2 – t1 (run)
=(0–20 m/s)( 60 – 40 s)
=-20 m/s20 s
= -1 m/s/s
ACCELERATION FORMULA, UNITS & POWER SHAPE
Acceleration =final speed – initial speed
final time – intial time
m/s, cm/min, km/h
s, min, hrm/s/s, cm/min/min, km/h/sSince: sp2 = final speed, sp1 = initial speedt2 = final time, t1 = initial timea
=
(spf – spi)
(tf – ti)
a =
(sp2 – sp1)
(t2 – t1)
ACCELERATION FORMULA, UNITS & POWER SHAPE
Acceleration =final speed – start speed
final time – start time
or xa DtDsp
÷Dsp = sp2 – sp1
Dt = t2 – t1
sp2=final speed, sp1=start speed t2=final time, t1=start time
Since: Then:
a =
D spD t
USING THE ACCELERATION POWER SHAPE
or x
a DtDsp
÷A kid is sledding down a hill. When he enters the course his speed is 10 m/s. After 2 seconds he has reached a speed of 26 m/s. What was his acceleration?
Given Formula Setup Solution
List Given InfoAnd Unknown:
sp1 = 10 m/ssp2 = 26 m/sDt = 2 sa= ?
Show Needed Equations:
a = ------------
Substitute with Units & Show Math:
a = --------------
Circles Answer with Units:
a =
a = 8 m/s/s
(sp2 – sp1)Dt
26 m/s-10 m/s
2 s16 m/s
2 s
FREEFALL AND GRAVITATIONAL ACCELERATION
Freefall: Objects falling due to gravity All objects accelerate at the same rate
due to gravity during freefall regardless of their mass Objects may reach terminal velocity sooner
due to air resistance Gravitational acceleration (g) = 9.8 m/s/s
on earth
USING THE ACCELERATION POWER SHAPE
or x
a DtDsp
÷A woman jumps from a plane. She opens her parachute five seconds later. How fast was she going when she opened her shoot (disregard air resistance)?
Given Formula Setup Solution
List Given InfoAnd Unknown:
Dsp = ??Dt = 5 sa= g=9.8 m/s/s
Show Needed Equations:
Dsp =
Substitute with Units & Show Math:
Dsp =
Circles Answer with Units:
Dsp = 49.2 m/sa · Dt 9.8 m/s/s · 5 s