Linear Motion

1
Linear Motion

• Physics
• Mr. Padilla

2
Linear Motion

• Speed
• Velocity
• Acceleration
• Free Fall

3
Motion is Relative

• All motion must be measured with respect to
  something.
• A car driving at 35mph is moving at 35 mi/h with
  respect to the road.
• Everything moves. Even things that appear to be
  at rest move.
• The Earth, Sun, your desk
• All motion is relative.

4
Question What is the impact speed when a car
moving at 100 km/h bumps into the rear of another
car traveling in the same direction at 98 km/h?
5
Displacement

• Ex A frog hops away from the river. When he
  starts his journey he is 2m from the river. After
  3min he is 5m from the river. What is his
  displacement?
• ?x xf - xi
• ?x 5m 2m 3m
• Displacement is NOT the same as distance
• Ex track

• Displacement is a change in position.
• We measure the displacement by comparing an
  objects starting location to its final location.
• Displacement final position initial position.
• ?x xf - xi

6
Displacement

• Ex2 An apple falls from a tree 4m off the
  ground. It hits a man on the head 1m before it
  hits the ground. What is its displacement.
  (Assume up is positive and down is negative)
• ?x xf - xi
• ?x 1m 4m -3m
• Displacement can be positive or negative.

7
Speed

• Speed is how fast something is moving or the rate
  distance is covered.
• Speed is measured in distance/time
• m/s, km/h, mi/h
• There are 2 types of speed

• Instantaneous speed
• The speed of an object at a given time.
• In your car this is shown on your speedometer
• Average Speed
• Total distance/time

8
Average Speed

• Average speed is the whole distance covered
  divided by the total time of travel.
• General definition
• Average speed total distance covered/time
  interval
• Speed ?x/?t (xf-xi)/(tf-ti)
• Distinguish between instantaneous speed and
  average speed
• On most trips, we experience a variety of speeds,
  so the average speed and instantaneous speed are
  often quite different.
• Is a fine for speeding based on ones average
  speed or instantaneous speed?

9
Finding Average Speed

• Example 1 If we travel 320 km in 4 hours, what
  is our average speed? If we drive at this average
  speed for 5 hours, how far will we go?
• Answer vavg 320 km/4 h 80 km/h.
• d vavg x time 80 km/h x 5 h 400 km.
• Example 2 A plane flies 600 km away from its
  base at 200 km/h, then flies back to its base at
  300 km/h. What is its average speed?
• Answer
• total distance traveled, d 2 x 600 km 1200
  km
• total time spent ( for the round trip), t (600
  km/200 km/h) (600 km/300 km/h) 3 h 2 h 5
  h.
• Average speed, vavg d/t 1200 km/5 h 240
  km/h.
• Tip start from the general definition for
  average speed!

10
Velocity

• Velocity is speed in a given direction.
• 70 mi/h is speed 70 mi/h north is velocity
• The same equation can be used to calculate both
• v d/t
• If something is moving at a constant velocity, it
  has constant speed and direction. straight line
  path

11
Question which car is moving with a constant
velocity? Constant speed? Why?
12
Acceleration

• Acceleration is the rate at which velocity
  changes.
• acceleration ?v/t
• Acceleration is measured in m/s2
• An object can be accelerated by changing its
  speed, direction, or both.
• We have no deceleration, just positive and
  negative acceleration.

13
Examples

• If the odometer in your car read 0 when you
  started and 35km half an hour later, what was
  your average speed?
• If a cheetah can maintain a speed of 25m/s for
  10. min, how far will he travel?

• Avg speed total d/t
• 35km/.5h 70 km/h
• v d/t
• 25m/s d/10min
• 25m/s d/600s
• 600s x 25 m/s d
• 15000m d

14
Examples 2

• A car goes from 10.0km/h to 45.0km/h in 3.00s.
  What is its acceleration?
• In 5.0 seconds, car A goes from 30.m/s to 39m/s.
  Car B goes from 0.0m/s to 9.0m/s. Which has
  greater acceleration?

• a ?v/t
• a
• (45km/h 10km/h)/(8.33x10-4 h)
• a 42000 km/h
• They both have the same acceleration.
• ?v 9m/s for A and B
• t 5s for A and B
• So a 9m/s/5s
• a 1.8 m/s2 for both.

15
Ex

• An airplane starts from rest and undergoes a
  constant acceleration of 4.8 m/s2for 15s before
  takeoff. A) what is its speed at take off? B)
  How long must the runway be?

• A) vf a?t vi
• vf (4.8 m/s2)(15s) 0m/s
• vf 72 m/s
• B) ?x ½a(?t)2 vi?t
• ?x½(4.8m/s2)(15s)2 (0m/s)(15s)
• ?x 540m

16
Acceleration Problems

1. A bike accelerates uniformly from rest to a speed
   of 7.10 m/s over a distance of 35.4 m. Determine
   the acceleration of the bike.
2. An engineer is designing the runway for an
   airport. Of the planes that will use the airport,
   the lowest acceleration rate is likely to be 3.00
   m/s2. The takeoff speed for this plane will be
   65.0 m/s. Assuming this minimum acceleration,
   what is the minimum allowed length for the runway?

17
Constant Acceleration

• Means that the velocity is changing at the same
  rate in each time segment
• With a constant acceleration, we can get some
  equations for velocity and displacement.

• Diplacement
• ?x ½(vi vf)?t
• ?x ½a(?t)2 vi?t
• Velocity
• vf a?t vi
• Final v after any displacement
• vf2 vi2 2a?x

18
Ex

• Jane pushes a stroller from rest with a constant
  accel. of .50 m/s2. What its velocity after it
  has gone 4.75m?
• vf2 vi2 2a?x
• vf2 (0m/s)2 2(.50 m/s2)(4.75m)
• vf2 4.75 m2/s2
• v(vf2) v(4.75 m2/s2)
• vf 2.2 m/s

19
Acceleration on Galileos Inclined Planes

• Galileos findings
• A ball rolls down an inclined plane with
  unchanging acceleration.
• The greater the slope of the incline, the greater
  the acceleration of the ball.
• If released from rest, the instantaneous speed of
  the ball at any given time acceleration x time.
  
• What is its acceleration if the incline is
  vertical?

20
Acceleration Formulas

• Things to remember

• a vf vi / t
• x ½ at2
• x vit ½ at2
• vf2 vi2 2ax
• vf a?t vi
• v x/t

• vf Final velocity
• vi Initial velocity
• Upward movement () for distance and
  acceleration
• Downward movement (-) for distance and
  acceleration

21
Free fall

• If a feather and a rock are dropped at the same
  time which will hit the ground faster? Why?
• What if there was no air resistance?
• Gravity causes all objects to accelerate at a
  constant rate.
• Acceleration due to gravity is 9.8 m/s2 or 32
  ft/s2
• Because gravity acts downward, we will make both
  of these values negative.

22
Free Fall

• When an object is dropped, does it accelerate?
• Yes, all falling objects experience acceleration
  due to gravity.
• An object acted on only by gravity is in free
  fall.
• Down () velocity
• Up (-) velocity

• Gravity accelerates all objects the same amount.
• Acceleration due to gravity g 9.8 m/s2
• The instantaneous velocity of any free falling
  object can be found using the equn.
• v gt or
• vf2 vi 2 2g x
• vf vi g t

23
How fast?

• An apple falls from a very tall tree. It falls
  for 3s. How fast is it moving after each second?
• v gt or v at
• v (9.8m/s2)(1s) 9.8 m/s
• v (9.8m/s2)(2s) 19.6 m/s
• v (9.8m/s2)(3s) 29.4m/s

24
How far?

• To find how far something goes in a given time,
  we need to know its average velocity
• Galileos finding from the inclined planes
  experiment
• The distance traveled by a uniformly accelerating
  object is proportional to the square of the time
  Distance traveled (1/2) x (acceleration) x
  (time2).
• For a freely falling object, x ½ gt2.
• An object that starts at rest is going 9.8m/s
  after 1s of free fall. What is its avg. v?
• (0m/s 9.8m/s)/2 4.9m/s
• How far then did it fall in that second?
• 4.9m

25
Thrown objects

• A ball thrown up into the air will slow down on
  its way up, at the same rate that it will speed
  up on its way down.
• What is the velocity of a thrown ball at the top
  of its arc? What is its acceleration?

26
Free Fall Distance

• Time (s)
• 0
• 1
• 2
• 3
• 4
• 5
• 6

• Distance Fallen (m)
• 0
• 4.9
• 19.6
• 44.1
• 78.4
• 122.5
• 176.4

27
Free Fall Distance

• To calculate how far an object falls in a given
  time, we use the equation
• x ½gt2
• How far will a monster truck fall in 10s?
• d (1/2)(9.8m/s2)(10s)2
• d (4.9m/s2)(100s2) 490m
• How far will a feather fall in that same time?
  (with no air resistance)
• The same distance.

28
Reaction Time

• With a partner and a meter stick, determine your
  reaction time.
• Have your partner drop a meter stick and catch it
  with youre your fingers.
• Use the measurement and the displacement equation
  to determine your reaction time.
• Include the calculations with your homework.