INTRO TO MOTION

PART 1

VECTORS, SCALARS, AND DISTANCE VS. DISPLACEMENT

Vectors and Scalars

• A scalar quantity has a value (magnitude). The direction is not defined or not important.
• Speed is a scalar quantity. Your speedometer provides only a number (magnitude) with no direction.
• Other examples of scalar quantities: mass, temperature, volume, distance and time

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• Vectors indicate magnitude and direction.
• Examples: position, velocity, acceleration & force.
• Signs (positive and negative) indicate direction.
• Typically, motion to the right is considered positive while motion to the left is considered negative.
• Motion up is considered positive, motion down is considered negative.

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Nicole Ferreira 07

• Origin 🡪 point where variables have a value of zero.
• Position/displacement 🡪 separation between an object and the origin; indicates direction of movement; position is a vector quantity

origin

vector

• An object can have a negative position

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1. In this picture, the runner is ________ to the left of the origin.
2. In this picture, the runner is 9 meters to the ___ of the tree.

5 meters

left

Distance vs. Displacement

Distance is the total length covered during a trip. (Scalar)

• symbol = d
• unit = any type of meter
• calculate by adding all segments together

d = AB + BC + CD + DE + EF

d = 6 + 2 + 3 + 1 + 1

d = 13 meters

Distance vs. Displacement

Displacement is a measure of how far and in what direction you are from a starting point. (Vector)

• symbol = Δx
• unit = any type of meter
• equation: Δx = x_f – x_i
• x_f = final position from start position
• x_i = start (initial) position

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Note: Δ is the Greek letter Delta, meaning “a change in”

Distance vs Displacement

100 m

200 m

0 m

When an object moves in a straight line,

distance = displacement

A football player runs 35 meters east before realizing he is running toward the wrong goal. He immediately changes direction and runs 23 meters west before getting tackled.

a) What distance did the athlete travel during the play?

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b) What is athlete’s displacement at the end of the play?

35 m

23 m

distance = 35 m + 23 m

distance = 58 m

∆x = x_f – x_i

x_i = 0

x_f = 35 – 23

x_f = 12 m

∆x = 12 – 0

∆x = 12m

Review

• Scalar
• Quantities described by a number/magnitude (speed, mass, time, etc.)
• Vector
• Scalar quantity plus a directions – usually shown as an arrow
• Distance
• How much ground has been covered during motion
• Displacement
• How far an object is from its original location

PART 2

SPEED, VELOCITY, AND AVERAGE VELOCITY VS. CONSTANT VELOCITY

Speed

• An object’s average speed is equal to
• speed = distance/time s = d/t
• s = speed – unit is m/s (meters per second)
• d = distance – unit is m (meters)
• t = time – unit is s (seconds)
• Speed does not take into account an object’s direction

Velocity

• Speed plus direction
• Examples:

60 m/s = speed

60 m/s northwest = velocity

• When an object moves at the same speed in the same direction, the object has constant velocity
• Example: Car on cruise control traveling in a straight line
• Same unit as speed (m/s)

Average Velocity

• Average velocity without constant motion (traveling at different speeds or directions)
• Defined as the change in position, divided by the time during which the change occurred
• Formula: v = ∆x / ∆t

v = velocity 🡪 unit is m/s

∆x (displacement) = x_f – x_i 🡪 unit is m

t = time 🡪 unit is s

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Sample Problems

1. James has an electronic Thomas the Tank Engine. Thomas travels a distance of 75 cm in 15 seconds.

What is Thomas’ speed during the time interval?

Use the GUESS Method:

Givens Unknown Equation Substitution Solution

d = 75 cm

= 0.75 m

t = 15 s

G

U

s = ?

E

S

S

s = 0.75

15

s = d

t

s = 0.05 m/s

2. A car travels at a rate of 15 m/s for 3 s. What is the displacement of the car?

Use the GUESS Method:

Givens Unknown Equation Substitution Solution

v = 15 m/s

t = 3 s

G

U

∆x = ?

E

S

S

15 = ∆x

3

v = ∆x

t

∆x = 45 m

3. Emily’s dog, Clifford, escapes from the yard and runs to the neighbor’s house covering 82 m in 20 s. He then realizes, he has not been fed and walks halfway back in 38 s.

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a) What is Clifford’s average speed during his entire trip? 

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d = 82 + 41 = 123m

t = 20 + 38 = 58s

G

U

s = ?

E

S

S

s = 123m

58s

s = d

t

s = 2.12 m/s

3. Emily’s dog, Clifford, escapes from the yard and runs to the neighbor’s house covering 82 m in 20 s. She then realizes, she has not been fed and walks halfway back in 38 s.

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b) What is Clifford’s average velocity during her entire trip?

x_i = 0

x_f = 82 – 41 = 41m

t = 58 s

G

U

v = ?

E

S

S

v = (41 – 0) = 41

58 58

v = ∆x = x_f - x_i

t t

v = 0.71 m/s

4. You ride your bike 1 m at 3 m/s and then another 1 m at 5m/s. Is your average velocity for the total 2m trip greater than, less than, or equal to 4 m/s?

Support your answer through a calculation.

v_av = 3.8 m/s

v_av < 4