All Right Let’s Start

• Gonna need to know the speed formula:• Speed = distance (d) / time (t)• 50 meters / 25 seconds = 2 m/s Got to know average speed: Total distance over total time: 50m + 25 m divided by 25 s + 15s + 35 s = 75 m / 75 s = 1 m/s

Then:

• Velocity vs. Speed• Scalars vs. Vectors• Displacement at a 90 degree angle• (a^ +b^)= c^• Distance vs displacement

Acceleration

• ALWAYS LIST THE GIVENS!!!!!!!!!!!!!• Formulas:• Vf- Vi / time • Ex: A car accelerates from 20 m/s to 25 m/s in

2.5 s. What is it’s rate of acceleration?• 25 m/s – 20 m/s / 2.5 s = 2 m/s ^• Remember** Acceleration can be negative

Like so:

• A car slows from 30 m/s to 15 m/s in 5 s. What is the rate of acceleration?

• GIVEN:• Vf = 15 m/s Vi = 30m/s t = 5 s• They want to know rate of acceleration (a)• Vf (15m/s) – Vi (30m/s) / 5 s = - 3m/s^

• Got it?

Now a little trickier

• Displacement: From rest• A car accelerates uniformly from rest to a

velocity of 20 m/s in 7s. How far did it travel in this time?

• We want to know displacement. (Distance)• So we use d= ½ (Vi + Vf)(t) = • Recall: This is when a is constant.

Displacement when already moving

• A car with an initial velocity of 5 m/s accelerates uniformly at a rate of 4 m/s^. Find the displacement after 6 s.

• We are already moving so we use this:• (t^) • d= (5m/s)(6s) + ½ (4m/s^)(6s^) • d= 102 m• Notice Final V doesn’t enter or matter!!!!!

Now for Velocity

• A car with an initial velocity of 4 m/s accelerates uniformly at the rate of 5 m/s^. What is the final velocity after 5 s?

• We want to know velocity• Velocity with constant a is:• Vf= Vi + (a) (t)• Vf= 4 m/s + (5m/s^) ( 5s) = 29 m/s

Now Final Velocity given d

• A car accelerates uniformly form rest at a rate of 4 m/s^. What is the velocity of the car after 65 m?

• Always write the givens. It tells us where to go• Equation:^= • Our Equation : = +(2)(4m/s^)(65m)• Solve Vf = + =22.8 m/s

Now on to FREE FALL

• Remember free fall is interested only in the effect of gravity.

• For our purposes we will use -9.8 m/s^ as our acceleration due to gravity.

• Let’s do distance first:• A ball from rest falls for 4 s. How far did the

ball travel?• d = ½ (t^)(a) (Remember a is every second)

Solve

• Easy: (a)• Then = -78.4 m • Now how about Velocity given distance?• A ball falls from rest 30 m above the floor.

How fast is it moving when it strikes the ground? B. How long until it strikes the ground?

We use the velocity equation

• Free Fall Velocity Equation• Vf^ = Vi^ + (2) (a) ( d)• Vf= 30m)• Vf =- 24.2 m/s or 24.2 m/s down

How about Time?

• Same problem• Solve for time (t)• Equation for free fall time.• Vf= Vi + (a) ( t)• Isolate by 1.subtracting Vi from both sides.• Vf-Vi= (a)(t)• Then dividing both side by a : Vf-Vi / a

And it looks like this:

• = 2.47 s • Remember just take your time and use the

correct formula.

Now for Horizontally launched projectiles

Treat X and Y separately Let’s consider perfectly horizontal at a constant velocity. (ALWAYS LIST GIVENS)• A ball is thrown horizontally off a cliff with a

height of 22m at a horizontal velocity of 2.0 m/s. How long before the ball hits the ground?

• First we have to find velocity: = )(-22m)

So

It’s a vertical equation so Vi = 0Vf = • Vf = = 20.77 m/s• Then we plug in time equation

(t) = 2.12 s

How about distance?

• How far from the edge did the ball land?• Horizontal Equation for distance (d ord)• + ½ (a) (t^)• Or 2.0m/s)(2.12s) + ½(0)(2.12^)• Or (2.0ms)(2.12 s) =4.2 m

WOOOOOOW!!!That’s a lot!

• Now for them gosh durn angles!!!!!!!• Remember: Solve x and Y separately!!!!!• We will use Cos and Sin buttons

1st Problem

• Jaynes throws a ball with a velocity of 10m/s at an angle of 30 to the horizon. How far will the ball go?

• First draw a diagram• Then list the trig functions• Then list the givens

Jaynes throws a ball with a velocity of 10 m/s at an angle of 30 degrees above the horizontal. How far will the ball go?

8.83 m

Picture

X Problem (COS)

Y Problem (SIN)

t

v

d

t

a

v

v

d

f

i

vtd

?30

sm /10

sm /10

30

sm /66.8)30cos(10

sm /0.5)30sin(10

Trig

sm /66.8

m0

sm /0.5

sm /0.5

2/8.9 sm

atvv if

t)8.9(0.50.5 t8.90.10

t

8.9

0.10

ts 02.1

s02.1

s02.1

)02.1)(66.8(dmd 83.8

Breanna tosses a Frisbee at 4 m/s at 40 degrees below the horizontal off of the top of a cliff. If the coin lands 4 meters from the cliff, how tall is the cliff?

4m/s

Picture

X Problem Y Problem

t

v

d

t

a

v

v

d

f

i

vtd

?sm /4

40

sm /06.3)40cos(4

sm /57.2)40sin(4

Trig

sm /06.3

sm /57.2

2/8.9 sm

2

2

1attvd i

2)30.1)(8.9(2

1)30.1(57.2 d

md 6.11

s30.1

s30.1

))(06.3(4 t

st

st

30.1

30.106.3/4

m4

m4

40

4 m/s

Caleb fires a gun at 300 m/s. What is its maximum range? (What’s the farthest that it can shoot?)

Picture

X Problem Y Problem

t

v

d

t

a

v

v

d

f

i

vtd

Trig

sm /1.212

sm /1.212

2/8.9 sm

atvv if

t8.91.2121.212

t8.92.424

s29.43

)29.43(1.212dmd 9181

?45

sm /300

sm /300

45

sm /1.212)45cos(300

sm /1.212)45sin(300

m0

sm /1.212st 29.43

s29.43

9181m

Also

• There will be some vocabulary.

Now to practice

• 1. A car driven by Amanda accelerates from rest to 20 m/s in 4 s. What is the rate of acceleration?

• 5 m/s^

• 2. A car driven by Mykayla slows from 40 m/s to 20 m/s in 5 s. What is the rate of acceleration?

• -4 m/s^

More

• 3.A car driven by Josh jumping a red light accelerates uniformly from rest to 25 m/s in 5 s. How far did it go in this time?

• 87.5 m

• 4. A car driven by Ryann accelerates uniformly accelerates from 20 m/s at a rate of 5m/s^. Find the displacement after 5 s.

• 162.5m

And more

• 5. A car driven by Timothy with an initial velocity of 10 m/s accelerates uniformly at 3 m/s^. What is the velocity after 6 s?

• 28m/s• 6. A car driven by Jesse accelerates uniformly

from rest at a rate of 5 m/s^. What is the velocity after 70m?

• 26.46 m/s

Keep going

• 7. A ball is dropped by Ian for 7 s. How far did the ball travel?• 137.2 m

• 8. A ball dropped by Elizabeth falls from rest 4 m to the floor. A. How fast was it going when it hit the floor? B. How long did it take to hit the floor?

• A.- 8.85 m/s• B.90 s

•

And going

• 9. A ball is thrown from a cliff by Media with a height of 20 m at a velocity of 5 m/s . How long before it hits the ground?

• 2.02 s

• 10. How far from the edge did the ball land?• 10.1m

ANGLES OH NO!!!!!!!!!

• Hunter throws Savannah at a velocity of 20 m/s at an angle of 25 degrees to the horizon. How far will she go?

• 31.1 m• Juan fires a rifle at 50 m/s. What is the farthest

the bullet will go?• 254.5 m