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