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Kinematics 1-D Motion. Vocabulary of Motion. Distance Scalar quantity Displacement Vector quantity, Object’s change in position. 5 km. Distance traveled = 15 km Displacement = 5 km, East. 5 km. 5 km. Vocabulary of Motion. Speed Scalar Quantity - Change in distance over time. - PowerPoint PPT Presentation
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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?