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 4 th 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. A 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 = m/s.

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?

The Kinematic Equations Equations used for uniform acceleration…

Kinematic Problems How much time does it take to accelerate from rest to 22.5 m/s at 1.5 m/s 2 ? Suppose you accelerate at 2.0 m/s 2 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 displacement time displacement

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 m/s 2 (roughly -10 m/s 2 ). This acceleration due to gravity is called g. Kinematic equations can be used to determine time (t), velocities (v i or v f ) or the height (d). GRAVITY

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 = m/s m/s +20 m/s +10 m/s 0 m/s - 10 m/s - 20 m/s - 30 m/s - 40m/s

Freefall Problems A ball is thrown upward at 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 directly proportional linear graph inversely proportional hyperbolic graph

directly proportional to the square parabolic graph inversely proportional to the square very steep hyperbolic graph Proportionalities