Famous train problems!

A train leaves Provo for SLC at 8:00 am, going 10 mph. A second express train leaves Provo for SLC at 9 am, going 15 mph. It is 40 miles to SLC. Will the 2nd train catch up before SLC? Where?

If someone on the first train looks back and sees the second train getting closer, with what speed does the gap between them narrow? This is the magnitude of the relative velocity (difference in velocities).

Acceleration

Position: where the object is.Displacement: change in position.Velocity: rate of change in position with time: instantaneous velocity is slope of x vs t graph.  Acceleration: rate of change in velocity with time

( ) slope of ( ) grapha t v t

avgvat

Some typical accelerationsa due to gravity near earth’s surface: g = 9.8 m/s2 (one “g”)

among major cities: Lowest in Mexico City (g = 9.779 m/s²) and highest in Oslo and Helsinki (g = 9.819 m/s²). Provo g = 9.799 m/s2

Some typical accelerationsSpace shuttle launch: 20 m/s2

Extreme amusement park rides 20 to 50 m/s2 in turns

Fighter pilots: 40 to 80 m/s2 in turns

Air Force’s Dr. John Stapp In 1954 he rode the "Sonic Wind" at 620 mph (280 m/s),

to a dead stop in 1.4 seconds. Max a: 45 g’s.

a is in the same direction as the force that causes v to change.

ReviewWhat do we mean by +/- position?being on the + or - side of the origin

What do we mean by +/- velocity?moving in the + or – direction. Change in position is +/- 

What do we mean by +/- acceleration? the change in velocity is in the + or – direction. 

New

Easier!

Easier!

If a is in same direction as v, speeds up If a is in opposite direction as v , slows down

Examples of acceleration direction or sign

If a is in same direction as v, speeds up If a is in opposite direction as v , slows downa is in the same direction as the force that causes v to

change.

A car moves left at constant speed. a is ____A car moving left is slowing down. a is ____A car moving left speeds up. a is ____

Paddle-bunji-ball

P1. What is the direction of a of the ball while traveling to your right and slowing down because the elastic stretches?

A. rightB. leftC. zero

P2. What is the direction of a when the ball is coming back (to your left, and speeding up)?

P3. What is the direction of a at the instant the ball is stopped by the elastic and about to start coming back?

Paddle-bunji-ballSketch a(t) for the ball being hit, going to right, and coming back.

Ball thrown upward into air

while throwing:

while it’s traveling up:

at the very top:

while falling down:

What is the direction of the acceleration…

Ball thrown upward into airSketch a(t) for the ball being thrown, going up, and coming back down.

“Free-falling” motion

acceleration is ______ with direction_________

…whenever object has only the force of gravity on it, whether going up or down

(have to neglect air friction…OK when v is small )

Whenever a is constantv(t) graph is a _______________

x(t) graph is a ________________

“Kinematic equations” for constant a case

2

2 2

or

2

122

f if i

f iav

av

i

f i

v vv v at a

t

v vv

x v t

x v t at

v v a x

Given on formula sheet for exams

A boy runs 50 m, starting at rest, with a constant acceleration of 0.25 m/s2. Find:a) the time it took b) his average velocityc) his final velocity 

◦Draw a diagram! ◦Label with symbols, numbers for “initial” and “final” cases◦Look for connection with equations.

Free-fall and kinematic equations

Acceleration due to gravitychoose positive direction, which determines whether g is + or – acceleration.

  A monkey drops from a tree and takes 2 sec to hit the ground. How far did the monkey drop? What was his average velocity?

Given only the information in the diagram, which single kinematic equation can be used to answer the following in one calculation:  P5) How long does it take to reach the top of its path?P6) What is the velocity when it was caught?P7) What was the average velocity for the motion?P8) How long does it take to hit the ground if you miss?

2

2 2

A.

B. 2

1C. 2

D. 2

E. More than one equ. is needed

f i

f iav

i

f i

v v at

v vv

y v t at

v v a y

milk drop demo yv

t

vat

Rocket Launch … a changes during trip

Accelerates upward with a1 by ejecting burning fuel for a time t1

Engines stop and rocket continues up, then falls to earth “without air friction”.

How long is the total time in the air?

How high did it go?

Concept reviewWhich of the following graphs represents 1. a bike moving at constant velocity2. a car speeding up then slowing down3. a ball thrown up in the air that comes back down4. a car that always speeds up5. a motorcycle that slows down and parks.  Careful! a, b are velocity v(t), and the others are position x(t)

Lecture 3, accelerationBasic concepts:

◦ a as slope of v(t)◦directions and signs of a, including when objects stop and reverse

Basic problems, skills:◦single step using a kinematic equation◦drawing good diagrams, using symbols

Advanced problems, skills:◦more than one step using kinematic equations◦using quadratic equation to find t, or using two kin. eqns. ◦using two different a’s in one problem