Transcript
Page 1: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

A. Kinematics in One Dimension

Page 2: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Mechanics – how & why objects move

Kinematics: the description of how objects move

Page 3: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

a. Distance: total length of travelb. Displacement: change in position

Let’s say a runner jogs a lap around a 100-meter track. He returns back to where he started in 4 minutes. a. What distance did he travel?b. What was his displacement?

Page 4: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Our Very First Formula! Isn’t this exciting?Displacement:

Δx = xf – xi ,

Where Δx = change in position, or displacement,xf = final position, and

xi = initial position*Displacement is directionally dependent! You CAN

have negative displacement!

Page 5: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Use a visual!

Page 6: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Does the odometer in your car measure distance or displacement?

Can you think of a situation where it would measure both?

Page 7: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

A particle moves from x = 1.0 m to x = -1.0 m. What is the distance? Displacement?

Page 8: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

You are driving around a circular track with a diameter of 40 m. You drive around 2 ½ times. How far have you driven? What is your displacement?

Page 9: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Speed & Velocity

Page 10: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

a. Average Speed = distance traveled / elapsed time of travelUnits: m/s

*Directionally Independent – always positive!

Page 11: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

You nose out another runner to win the 100.000 m dash. If your total time for the race was 11.800 s and you aced out the other runner by 0.001 s, by how many meters did you win?

Page 12: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Velocity: speed AND direction

Page 13: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Velocity = displacement/elapsed time Units: m/s

Directionally DEPENDENT! Pick your frame of reference – which way is positive & which is negative?

Page 14: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Your friend Marsha lives 0.55km east of your house. The nearest grocery store is 0.82km west of your house. You walk from your house to the grocery store for some soda. It takes you 17 minutes to get there, and you spend 3 minutes in the store. Then, in 12 minutes, you walk from the grocery store over to Marsha’s house. Find the distance you traveled, your displacement, your average speed, and your average velocity.

Page 15: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Graph position vs. time for your trip to the grocery store & Marsha’s house.

The slope of the line along each interval shows your velocity!

Page 16: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Describe the object’s motion along each interval.

Page 17: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Instantaneous velocity is an object’s speed at a point in time.

On a position vs. time graph, it equals the slope of the tangent line at any time.

Page 18: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move
Page 19: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

t(s) x(m)

0 0

0.25 9.85

0.50 17.2

0.75 22.3

1.00 25.6

1.25 27.4

1.50 28.1

1.75 28.0

2.00 27.4

Page 20: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Acceleration

Page 21: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Review: v=Δd/Δta. Acceleration: how quickly an object’s velocity

changesb. Acceleration can be:

a. Speeding up (v and a are in same direction)b. Slowing down (different sign for v and a)c. Changing direction (2-D motion)

Page 22: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Units for acceleration are m/s2

In Physics B, we assume acceleration is constant.

Page 23: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Saab advertises a car that goes from 0 to 60.0 mi/h in 6.2s. What is the average acceleration of this car?

An airplane has an average acceleration of 5.6 m/s2 during takeoff. How long does it take for the plane to reach a speed of 150 mi/h?

Page 24: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

Instantaneous acceleration can be found by calculating the slope of the tangent line at a point on a velocity vs. time graph.

Constant acceleration (in an ideal world): instantaneous a = average a

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Kinematic Equations

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Page 27: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

A car slows down along the road from 40.0 km/h to 24.0 km/h in just 3.70 seconds. What is the car’s acceleration?

A ball is thrown into the air at a velocity of 15.0 m/s. It is caught at the same height when it is traveling downward at a speed of 15.0 m/s. Find the average velocity of the ball.

Page 28: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

A ball is dropped (not thrown) from a height of 77.2m. How long does it take to hit the ground below? (neglect air resistance and remember gravitational acceleration= 9.81m/s2)

A skydiver is falling at a velocity of 8.2 m/s downward. The parachute is opened, and after falling 19m, the skydiver is falling at a rate of 2.7m/s. What deceleration did the parachute provide?

Page 29: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

1. A child slides down a hill on a sled with an acceleration of 1.5 m/s2. If she starts at rest, how far has she traveled in (a) 1.0s, (b) 2.0s, and (c) 3.0s?

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2. On a ride at an amusement park, passengers accelerate straight downward from zero to 45mi/h in 2.2s. What is the average acceleration of passengers on this ride?

Page 31: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

4. Two cars drive on a straight highway. At time t=0, car 1 passes mile marker 0 traveling due east with a speed of 20.0 m/s. At the same time, car 2 is 1.0 km east of mile marker 0 traveling at 30.0 m/s due west. Car 1 is speeding up with an acceleration of magnitude 2.5 m/s2, and car 2 is slowing down with an acceleration of magnitude 3.2 m/s2. Write x-versus-t equations of motion for both cars.

Page 32: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

5. You’re driving around town at 12.0 m/s when a kid runs out in front of your car. You brake – your car decelerates at 3.5 m/s/s.

(a)How far do you travel before stopping? (b)When you have traveled half that distance,

what is your speed? (c)How much time does it take to stop?(d)After braking half that time, what is your

speed?

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Page 34: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move
Page 35: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

a. Objects of different masses/weights fall with the SAME ACCELERATION(at sea level & neglecting air resistance)

b. What acts on an object in free fall?-NOTHING but gravity (hence the free)

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c. Objects in free fall can move down, OR up!

d. g = 9.81 m/s/s ← g is always positive 9.81 m/s/s. If your frame of reference says down is negative, use –g.

*If down is positive and x0=0, then x=1/2 gt2

(derived from that super-important eqn)

Page 37: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

At what acceleration does a 5000kg elephant fall?

What about a mouse?

Page 38: A. Kinematics in One Dimension.  Mechanics – how & why objects move  Kinematics: the description of how objects move

You drop a ball from a 120-m high cliff• How long is it in the air?

• What is its speed just before it hits the ground? (at x=0m)

• Sketch x vs t, v vs t, and a vs t graphs for this


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