Linear Motion. Objectives Understand the concept of relative motion. Know the distinction between...

Linear Motion

Objectives

• Understand the concept of relative motion.• Know the distinction between distance and

displacement.• Understand the concepts of average velocity

and average speed.• Be able to solve simple velocity or speed

problems.

Relative Motion and Time

• Is the apple moving?

• All motion is relative; it must be compared to other objects (matter and space).

• time: a 4th dimension in which events (motion) occur• Time and space are closely related: how do you

know time has passed if there is no motion?

Displacement and Distance

• displacement: a change in position (vector)• distance: how far something travels (scalar)• We tend to say distance when we mean displacement.

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B

Average Velocity and Speed

• average velocity: displacement during unit of time (m/s, mph); velocity is a vector quantity (specific direction)

• average speed: total distance covered over a time interval; speed is a scalar quantity (no direction)

• What is the average speed (in mph and m/s) if it takes 4 hr 42 min to drive the 268 miles to Bozeman, including breaks? 1.00 mph = 0.447 m/s.

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Indicating Velocity

• Consider a collision between two cars, one traveling at 55 mph and the other at 57 mph. Is it a bad wreck?

• It depends on the direction!

• We represent direction using +/- signs or vectors.

Objectives

• Understand the concept of acceleration.• Be able to solve acceleration problems using

the kinematic equations.

Acceleration

• acceleration: a change in velocity over a time interval; vector quantity

• You can accelerate by (1) speeding up, (2) slowing down, or (3) changing direction.

• A ball is rolled up an incline at 4.6 m/s. 3.5 seconds later it is rolling down at 2.8 m/s. What is the acceleration?

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The Kinematic Equations

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Equations used for uniform acceleration…

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Kinematic Problems

• How much time does it take to accelerate from rest to 22.5 m/s at 1.5 m/s2?

• Suppose you accelerate at 2.0 m/s2 from 15 m/s to 21 m/s. How much distance is covered?

Motion Graphs: Slope

• The slope of a graph = rise/run.• This slope represents d/t, or velocity!• A constant slope means a constant

velocity• A changing slope means a changing

velocity (an acceleration).

time

disp

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time

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Motion Graphs: Area• For a velocity vs. time

graph, the area-under-the-curve equals v · t, or displacement.

• Notice how the area (displacement) is proportional to time squared.

• Galileo discovered this!time

velocity

Objectives

• Understand the concept of freefall.• Be able to solve freefall problems using the

kinematic equations.

Free Fall

• Due to gravity, objects accelerate at -9.81 m/s2 (roughly -10 m/s2).

• This acceleration due to gravity is called g.

• Kinematic equations can be used to determine time (t), velocities (vi or vf) or the height (d).

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Free Fall: Velocity

• If you throw a ball upwards at +30 m/s, it will accelerate at g.

• Just keep taking -10 m/s from the velocity each second.

• When solving problems, use g = -9.81 m/s2.

+30 m/s

+20 m/s

+10 m/s0 m/s

- 10 m/s

- 20 m/s

- 30 m/s

- 40m/s

Freefall Problems

• A ball is thrown upward at +25.2 m/s. What is its height after 3.8 seconds?

• How deep is a well if it takes 4.6 seconds for a rock to fall to the bottom?

Proportionalities

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xy ~

directly proportional

linear graph

inversely proportional

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hyperbolic graphxy 1~

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2~ xy

directly proportional to the square

parabolic graph

inversely proportional to the square

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Proportionalities