Kinematics 1-D Motion

Vocabulary of Motion

• Distance–Scalar quantity

• Displacement–Vector quantity, Object’s

change in position

• Distance traveled = 15 km• Displacement = 5 km, East

5 km

5 km

5 km

Vocabulary of Motion

• Speed–Scalar Quantity- Change in distance over time

Vocabulary of Motion

• Velocity–Vector Quantity

– Average Velocity =

v = Change in Position = Δd

Change in Time Δt

Vocabulary of Motion

• Acceleration–Vector Quantity

a = Change in Velocity = Δv

Change in Time Δt

- Positive a – speeding up

- Negative a – slowing down

Motion Graphs

• Position Vs. Time

Pos

ition

TimeObject is

Stopped, v = 0

Pos

ition

Timev = + constant

• Position Vs. Time

Pos

ition

Time

v = - constant

• (Not constant velocity)P

ositi

on

Time

Object is decreasing speed

over time

Pos

ition

Time

Pos

ition

Time

Object is increasing speed

over timeP

ositi

on

TimeWalks away. Stops, walks back towards

start and keeps going past 0, -.

Pos

ition

Time

Constant speed, slowing down to a stop, then

increasing speed

Slope?

• The slope of a Position vs. Time graph is the objects Velocity!

Slope = Δy = Δd = v

Δx = Δt

Which graph best represents the motion of a block accelerating uniformly

down an inclined plane?

Motion Graphs

• Velocity vs. Time

Time

Vel

ocity

Velocity is constantTime

Vel

ocity

Increasing at a constant rate, +

Time

Vel

ocity

Velocity is decreasing at a constant rate, -

Time

Vel

ocity

Velocity is decreasing, stops and

increases in the other direction

Slope?

• The slope of a velocity vs. Time graph is its acceleration!

Slope = Δy = Δv = a

Δx = Δt

Mathematical Analysis

• Finding Average Velocity

v = vi + vf or Δd

2 Δt

Note: vi = Initial Velocity

vf = Final Velocity

• Acceleration

a = Δv or vf – vi

Δt Δt

Problems

• A car travels 650 m in 5.0 sec. What is its average velocity??

Problems• A car starting at rest accelerates at

2.0 m/s2 for 2.0 sec. What is its final velocity?

• A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.

• Area Under Velocity vs. Time graph is the distance traveled

Additional Motion Equations

• d = vit + 1/2at2

• vf2 = vi

2 + 2ad

On Your Own

• A car is traveling at 35 m/s. It then accelerates at a rate of 6.0 m/s2 for 10 sec. Find the final velocity of the car.

FREE FALLING!

Free Fall

• All bodies fall at the same rate of acceleration

• The acceleration due to gravity near the Earth’s surface is 9.81 m/s2

What does that mean?

• Every second an object falls, its speed is increasing by 9.81 m/s

t = 0 sec, v = 0 m/s

t = 1 sec, v = 9.81 (10) m/s

t = 2 sec, v = 19.62 (20) m/s

t = 3 sec, v = 29.43 (30) m/s

Motion GraphsP

ositi

on

Time TimeV

eloc

ity

Mathematical Analysis of Free Fall

• a = g = 9.81 m/s2

• For an object being dropped, The initial velocity is ZERO.

• Motion in the y-direction (vertical)

Problem . . .

• A 100 kg object is dropped from 10 m. How long does it take to hit?

• What is the final speed right before it hits the ground?