Friday 8/23 Notes

For those who went on the band trip

1. Average Velocity

The average velocity is the rate at which displacement occurs

• Usually ti = 0

• Velocity and displacement are in same direction (+ or -)

• Units: m/s, mph

Δt

xx

Δt

Δxv ifaverage

Average VelocityAverage velocityAverage velocity equals equals the slope of the line the slope of the line joiningjoining the initial and final positions (on x-t graph) the initial and final positions (on x-t graph)

ProblemExample 2.2 (page 30)

2. Instantaneous Velocity

• Instantaneous velocity = the velocity at a specific point in time

• Ex: Speedometer

• The limit of the average velocity as the time interval becomes infinitesimally

• short (Δt 0)

Instantaneous VelocityInstantaneous velocityInstantaneous velocity is the is the slope of the slope of the tangenttangent to the curve at the time of interest to the curve at the time of interest

Note:The instantaneous velocity of a point on a line is the slope of the line it is

on.

3. Constant Velocity• Velocity does not change over time• Ex: car on cruise control

Speed

• Speed is a scalar quantity– same units as velocity– total distance / total time–No direction required

Example

• My drive to school:

Average Velocity vs.

Instantaneous Velocity

What is my average velocity?

I live about 25 miles from school,and the drive takes about 30 minutes.

During the trip, I drive 2 miles @ 30 mph,stop at a light for 1 minute, accelerate to 60 mph and continue for 20 miles, stop at a light for 1 more minute, drive 45 mph for 3 miles, and then park.

What is my average speed?What is my average speed?

Answer: solve for time in each,then vavg = (total x) / (total t)

• 2 mi @ 30 mph = 4 min• Stoplight = 1 min• 20 mi @ 60 mph = 20 min• Stoplight = 1 min• 3 mi @ 45 mph = 4 min

Total X = 2 + 0 + 20 + 0 + 3

Total time = 4 + 1 + 20 + 1 + 4

Vavg = 25 mi / 30 min = 25 mi / 0.5 hr = 50 mi/hr