Acceleration

1
Acceleration

• Recall, the average acceleration is the rate of
  change of velocity between a change in time and
  is represented by the following equation.

2
Constant Acceleration

• If an object undergoes uniform motion, or
  constant velocity, and the slope of the
  position-time graph is constant, then the object
  is undergoing
• Constant Acceleration

3
Instantaneous Acceleration

• If the slope is not constant and it has a curve,
  then we say that we have an
• Instantaneous Acceleration

4
Positive and Negative Acceleration

• Consider a ball rolling up a driveway. What
  happens to the acceleration?
• It slows down, stops briefly, and rolls back down
  the driveway.
• What do you think the graphs would look like?

5
(No Transcript)
6
Practice Problems

• An Indy 500 race cars velocity increases from 4
  m/s to 36 m/s over a 4.0-s time interval. What
  is the Acceleration?
• Start writing out what you have and know.
• Vi 4 m/s
• Vf 36 m/s
• T 4-s
• A ?

7
Answer
8
Question 2

• The race car slows down form 36 m/s to 15 m/s
  over 3 seconds. What is the average
  acceleration?
• Vi 36 m/s
• Vf 15 m/s
• T 3-s
• A ?

9
Answer
10
Question 3

• A bus is moving at 25 m/s when the driver steps
  on the brakes to avoid hitting Kevins tricycle.
  The bus driver brings the bus to a stop in 3.0
  seconds.
• A) What is the average acceleration of the bus
  while breaking?
• B) If the bus took twice as long to stop, how
  would the acceleration compare with what you
  found from part A?

11
Acceleration when instantaneous velocity is zero.

• What happens to the acceleration when velocity
  zero, that is, when the ball in the example
  problem stops and reverses its direction?
• Remember that the velocity is zero only at an
  instant of time, not for an instant.

12
Calculating Velocity from Acceleration.

• V velocity
• T any moment in time
• Vi initial velocity
• A constant acceleration

13
Velocity with Constant Acceleration Formula

• V Vi at

14
Practice Problems

• A golf ball rolls up a hill toward a
  miniature-golf hole. Assign the direction toward
  the hole is positive.
• A) If the ball starts with a speed of 2.0 m/s and
  slows at a constant rate of .50 m/s², what is its
  velocity after 2.0 seconds.
• Tell me, what should you do first!

15
Answer

• Write down what you have.
• Vi 2.0 m/s
• A .50 m/s²
• T 2.0-s
• V ?
• V 2.0 (.50)(2.0)
• V 3 m/s

16

• B) If the constant acceleration continues for 6.0
  seconds, what will be its velcity?
• V 2.0 (.50)(6)
• V 4 m/s

17
Practice Problem

• A bus, traveling at 30 km/hr, speeds up at a
  constant rate of 3.5 m/s². What velocity does it
  reach 6.8-s later?
• Vi 30 km/hr 8.3 m/s
• A 3.5 m/s²
• T 6.8-s
• V ?

18
Problem Again

• If a car accelerates from rest at a constant 5.5
  m/s², how long will it need to reach a velocity
  of 28 m/s?
• Write down what you know and what you are looking
  for.
• Solve.

19
Displacement under Constant Acceleration

• Final Position with Constant Acceleration.
• D (1/2) (Vf Vi)t
• D (Vi)(t) (1/2)(a)(t²)
• What is the difference between the two formulas?
• One contains acceleration and the other does not.

20
Hey look, more formulas ?!!!?

• Vf Vi at (review)
• Vf² Vi² 2(a)(d)
• Again, notice the difference.

21
Problem

• Kevins yellow Saturn starts at rest and speeds
  up at 3.5 m/s² after the traffic light turns
  green. How far will it have gone when it is
  going 25 m/s?
• Write what you know and what you want!!!!
• Vi 0 m/s
• A 3.5 m/s²
• Vf 25 m/s
• D ?

22
Answer

• Which formula?
• Vf² Vi² 2(a)(d)
• 89 m

23
Problem 2

• A race car traveling at 44 m/s slows at a
  constant rate to a velocity of 22 m/s over 11-s.
  How far does it move during this time?
• Vi 44 m/s
• Vf 22 m/s
• T 11-s
• D ?
• Which Formula?

24
Problem 2

• An Airplane starts from rest and accelerates at a
  constant 3.00 m/s² for 30 seconds before leaving
  ground.
• A) How far did it move?
• B) How fast was it going when it took off?

25
Free Fall

• Do larger objects fall faster than smaller
  objects?
• No they fall at the same rate. You can thank
  Galileo for that.
• He said, if you neglect air resistance, all
  objects, regardless to size, fall with the same
  acceleration.

26
The g - Gravity

• The magnitude of falling objects is given the
  special symbol g equal to 9.8 m/s²
• Note that g is a positive quantity. You will
  never use a negative value for g in a problem
  even if the motion is going down.
• But what if you throw something straight up?
• g would be negative because it is going against
  gravity.

27
Acceleration due to gravity

• Acceleration due to gravity is the acceleration
  of an object in free fall that results from the
  influence to Earths gravity.

28
I dropped my rock.

• Suppose you drop a rock. One second later, its
  velocity is 9.8 m/s. Two seconds later it
  velocity is 19.6 m/s. Why?
• The acceleration is constant.
• 9.8 m/s²
• What would the velocity of the rock be after 3
  seconds?

29
Formulas.

• Vf Vi (g)(t)
• Vf² Vi² 2(g)(d)
• D Vi(t) (1/2)(g)(t²)

30
Problem

• The demon drop ride at Ceder Point Amusement park
  falls freely for 1.5s after starting from rest.
• A) What is the velocity after 1.5 seconds?
• B) How far does it fall?
• Which formula?