Motion in One Dimension AKA… Linear Motion

One-Dimensional Motion ______________ motion takes place only in one direction. Example: The train can move either forward or backward along the tracks. It cannot move left or right. In another words… An object can move _______ or ________, but not ____________ and _________ at the same time.

Frame of Reference ______________ – a system for specifying the precise location of objects in space and time “Another words, a reference point to measure _________________.” Example: ___________________

Distance Is a _______ quantity Has _________, but no _________ Measures the _______ between two objects without indicating _______ from each other Example: _____________________

Displacement A _______ quantity Has __________ and ___________ ____________ – change in position of an object Units: ___________ Displacement =

Example of Displacement Displacement is _____ always equal to the distance traveled. Example if you walk three steps forward, and three steps back… Your distance is ???? Your magnitude is _______!

Displacement Continued Displacement can be ______ or ______ Unless otherwise stated, Displacement to the right is ______ Displacement to the left is ______ Upward displacement is _______ Downward displacement is _______ Examples: _______________________

Can be Pos or Neg…

1. MOTION IS RELATIVE Everything moves, at least with respect to some reference point. To describe motion we shall talk about ___________

is the speed you would read from a speedometer. Average Speed = ___________ Units – _____________

Example of Average Speed 30 mph A B 2 miles ? You take a trip from A to B and back to A. You want to average 60 mph for the round trip A to B to A. From A to B you average 30 mph. What is your average speed on the return trip from B to A?

Example of Average Speed 30 mph A B 2 miles ? 60 mi/hr is 60 mi/(60 min) or 1 mi/min. To average 1 mi/min for a 4 mi trip would require 4 min. 30 mi/hr is 30 mi/(60 min) or 1 mi/(2 min). A 2 mi trip would take 4 min. See a problem???

Speeding Little Old Lady Sorry, Ma’am, but you were doing 45 mph in a 30 mph zone. Okay, okay, would you believe that I haven’t been driving for an hour yet? But I haven’t driven 45 miles yet.

3. Velocity Average Velocity = ______________ Units - _________________ Instantaneous Velocity of an object is its _____________ plus the __________ it is traveling. Velocity is a _________.

Speed vs. Velocity Velocity is NOT the same as speed. Speed has ________ only (how fast) Example: _______ Velocity has _______ and _______ Example: ____________ **** +/- can serve as a direction

Average Velocity Units: meters per second, m/s Average Velocity = change in position change in time Vavg = Δ x = xf − xi Δ t tf − ti

Displacement and Average Velocity Distance traveled is the length of the path taken. Average velocity =

Velocity can be interpreted Graphically When an object’s position is plotted versus time, the _____ of a position-time graph is the object’s velocity.

Instantaneous Velocity is NOT Average Velocity Instantaneous Velocity is the velocity of an object at ________________ Example: When you glance down at your speedometer while driving, the speed indicated by the speedometer is the magnitude of your instantaneous velocity. (or how fast you are going at that instant)

4. Acceleration Acceleration = __________________ Units – Acceleration is also a ________. Has both magnitude and direction

Motion at constant velocity Accelerated motion Here Here, too

Demo - Ball on incline and ball on table We can sense acceleration by comparing observations from a constant velocity frame of reference to observations from an accelerating frame of reference. Interpretation - we can feel acceleration if there is a “support” force or contact.

Acceleration on Galileo's Inclined Planes

Velocity and Acceleration Galileo used ____________ to study accelerations. He found constant accelerations for inclines: the _______ the incline, the _______ the acceleration. (It was too hard to measure time for free-falls.) He also found that the size of the objects ______ matter.

Average Acceleration Average Acceleration = aavg = Units: ________

Determining Acceleration Graphically When a graph of an object’s velocity over time is produced, the slope of the _____________ graph is the acceleration of the object. When the velocity of an object is constant, the acceleration is _____.

Velocity and Acceleration An object with a + velocity and + acceleration is __________ An object with a + velocity and - acceleration is __________ An object with a - velocity and - acceleration is __________ An object with a - velocity and + acceleration is __________

Negative Values A negative value for the acceleration of an object does not always indicate that the object is decelerating. If the object is traveling in the negative direction, a negative acceleration would result in the object moving ________ in the _______ direction.

Relationships Between v and a for Linear Motion. If initial velocity is zero, then

Example A jogger starts at zero velocity with an acceleration of 3 ft/s2. How fast is she moving after 4 seconds? (Let’s see if we can first do this without using any equations.)

Chapter 3 Review Questions

What is the average speed of a horse that gallops a round-trip distance of 15 km in a time of 30 min? (a) 0 (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

What is the average velocity for the round-trip of the horse in the previous question? (b) 0.5 km/h (c) 30 km/h (d) 500 m/s (e) None of the above

Some formulas relating to displacement, velocity, and acceleration: Finding Displacement with Constant Uniform Acceleration ∆x = ½ (Vi + Vf) ∆t Finding Final Velocity with Constant Uniform Acceleration Vf = Vi + a∆t

Formulas Continued Finding Displacement with Constant Uniform Acceleration ∆x = vi∆t + ½ a (∆t)2 Finding Final Velocity after Displacement Vf2 = Vi2 + 2a∆x

5. FREE FALL Motion near the surface of the earth in the absence of air resistance, ______ ___________________________. The acceleration of an object is g = __________ = _____________.

David Scott and the moon David Scott demonstrated this on the moon in 1971 when he dropped a hammer and a feather at the same time. Both the hammer and the feather landed on the moon’s surface at _____________ time.

A Ball thrown upward: While its velocity is positive (up), the acceleration on the ball is negative (down), so the ball ____________ as it climbs. At the top of the balls flight, its velocity is reduced to zero, but its acceleration will still be _________ (downward). As the ball falls, its velocity is ______ (down) and its acceleration is ______ (down), so the ball ____________.