Kinematics (Part 2)

Position

Position = a location with respect to the origin or zero point.

Negative and positive values are used to show direction from the origin.

Numbers with a direction are a vector quantity.

Finding Position

4 mile

s

6 mile

s0

6-4104

00-6-10

Position depends on where you put ‘0’.

Distance vs. Displacement

Distance: Total length of travel (direction is not considered so distance is a scalar quantity)

Displacement: Change in position (direction matters so displacement is a vector quantity)

• Δd = df – di

• df : final position (where you end)

• di: initial position (where you start)

• Can be negative if df <di

Example 1

4 mile

s

6 mile

s0 104You travel from home to the movies then out to dinner. (A)What is the distance traveled? (B) What is your displacement?(A) Distance = 4 +6 +6 = 16 miles(B)Displacement= df – di = 4 - 0 = 4 miles

Example 2

4 mile

s

6 mile

s0 10

4You left the movies, went home, went to dinner, then went to another movie. (A)distance traveled? (B) displacement?(A) Distance =6+4 +4 +6 = 20 miles(B)Displacement= df – di = 10 -10 = 0 miles

Example 3

4 mile

s

6 mile

s 6-4 0You start at home, go to dinner and then go to a movie.(A)distance traveled? (B) displacement?(A) Distance =4+6 = 10 miles

(B) Displacement= df – di = 6-(-4)= 10 miles

Quick Quiz Questions A - C

(A)What is the position of your keys?-10

(B)What is the position of your dog?-3

(C)What is the position of the flowers?0

7 mile

s

3mile

s? ? 0

Quick Quiz Questions D & E

7 mile

s

3mile

s? ? 0

You pick up your keys, then pick some flowers and give them to your dog.(D)What distance did you travel?

13 miles(E) What is your displacement?

-3 – (-10) = +7

F. What can be said about the motion displayed in this diagram?

It shows the runner is slowing down.

Quick Quiz Question F

3 VERY IMPORTANT EQUATIONS… GET YOUR

FORMULA CARD

Solving Kinematics Problems

Average Velocity

Vector QuantityCould have a negative valueChange in position divided by change in timeΔ = delta “change in”

v = Δ d (df – di) “f” = final or end

Δ t (tf – ti) “i” = initialUnits are things like (mi/hr, km/hr, m/s)

Distance

Scalar QuantitySimple manipulation of previous equation

Δ D = v x Δ t

Units are things like (m, km, mi)

Average Acceleration

Vector QuantityChange in velocity divided by change in time

a = Δ v (vf – vi)

Δ t (tf – ti)

Units are m/s2

USE THE GUESS METHOD

Solving Kinematics Problems

GUESS Method

A systematic way to not only show the correct answer, but also to display your physics knowledge

“G” – write down what is given“U” – write down the unknown“E” – write down the equation to be used“S” – substitute values into equation“S” – solve the problem

Example Problem #1

How long will it take to travel 50.0 miles in a cartraveling at 65 mi/hr?d= 50.0 milesv= 65 mi/hr

t=?s

Δd = v x t so… t = Δd/v

t= (50.0mi)/(65mi/hr)

t= 0.77 hr

Example Problem #2

A car is traveling at 18.5 m/s. The driver steps on the gas to pass a garbage truck. After 5.0 seconds, the car is traveling at 24.5 m/s. What is the car’s rate of acceleration?

vi = 18.5 m/s

vf = 24.5 m/s

t = 5.0 s

a = ???a = Δv / Δt

a = (24.5 m/s – 18.5 m/s) (5.0 sec)

a = 1.2 m/s2