chapter 2. clear and precise description of motion average speed instantaneous speed velocity...

Chapter 2

Average speed Instantaneous speed VelocityAcceleration

SpeedSpeed is how fast something is moving.

Average speed is total distance divided by the time of travel.

average speed = distance traveled

time of travel

Units of speed: MPH, km/hr, m/s, etc

Speed Unit Conversion

Example: (2.1 p 20)Convert 90 kilometers per hour to (a) miles per hour, and(b) meters per second

1 mile = 1.609 km1 km = 0.6214 miles1 hour =60 minutes1 minute =60 second

Average speed from Kingman to Flagstaff (50mph)

Average speed from Flagstaff to Phoenix (54mph)

Average speed from Kingman to Phoenix(52mph)

Average speed is the rate at which distance is covered over time.

Instantaneous Speed

Instantaneous speed is the speed at that precise instant in time.

It can be calculated as the average speed over a short enough time that the speed does not change much.

The speedometer tells us how fast we are going at a given instant in time.

Velocity

Velocity involves both the direction of the motion and how fast the object is moving.

Velocity is a vector .Velocity has a magnitude (the speed) and

also a direction of motion.A change in velocity can be a change in either the object’s speed or the direction of motion.

A car goes around a curve at constant speed. Is the car’s velocity changing?

Example

A force is required to change either the magnitude (speed) or the direction of the velocity.

Instantaneous velocity is the velocity at the precise instant. Size - equal to instantaneous speed Direction - equal to the direction of motion at that instant.

AccelerationAcceleration is the rate at which velocity changes.Acceleration can be either a change in the

object’s speed or a change in the direction of motion (it is a vector).

Acceleration can be either positive or negative.

acceleration = change in velocity

elapsed time

a vt

Average acceleration and instantaneous acceleration

Acceleration (cont.)

The direction of the acceleration vector is that of the change in velocity, ∆v.

If velocity is increasing (decreasing), the acceleration is in the same (opposite) direction as the velocity.

Acceleration (cont.)

What is the direction of the acceleration? At the right angles to the velocity.

• If a car goes around a curve at constant speed, is it accelerating? Why?

A car starting from rest, accelerates to a velocity of 20 m/s due east in a time of 5 s. What is it average acceleration?

Acceleration Units: velocity divided by time

Exercises (p 36):E2.9 A car travels with an average speed

of 58MPH. What is the speed in km/h?(1 mile=1.61 km)

E2.11 Starting from rest, a car accelerates at a rate of 4.2 m/s/s for a time of 5 seconds. What is the velocity at the end of this time?

Graphing Motion

To describe the car’s motion, we can note the car’s position every 5 seconds.

Time Position

0 s 0 cm

5 s 4.1 cm

10 s 7.9 cm

15 s 12.1 cm

20 s 16.0 cm

25 s 16.0 cm

30 s 16.0 cm

35 s 18.0 cm

We can graph the data in the table, let the horizontal axis represent time, and the vertical axis represent distance .

What can this graph tell us? D, v, a The graph displays information in a more useful manner than a simple table.

The slope at any point on the distance-versus-time graph represents the instantaneous velocity at that time.

Slope is change in vertical quantity divided by change in horizontal quantity.

“rise over run”

Steepness of slope, Zero slope , Negative slope

A car moves a long a straight line so that its position varies with time as described by the graph here. A. Does the car ever go backward?B. Is the instantaneous velocity at point A greater or less than that at point B?

Example (Q19, p35)

Horizontal axis represent time, and the vertical axis represent velocity.

Velocity-versus-time Graph

What can this graph tell us?D, v, a (How can we find the distance ?)

In the graph shown here, velocity is plotted as a function of time for an object traveling in a straight line.

Example (Q18, p 35)

The slope of the velocity-versus-time graph is the acceleration

a.Is the velocity constant during any time interval shown? b.During which time interval is the acceleration greatest?

A car moves along a straight section of road so its velocity varies with time as shown in the graph.

Example (Q21 p 35).

a. Does the car ever go backward?

b. At which point of the graph, is the magnitude of the acceleration the greatest?

A car moves along a straight section of road so its velocity varies with time as shown in the graph.

Example (Q22 p 35).

In which of the equal time segments, 0-2 seconds, 2-4 seconds, or 4-6 seconds, is the distance traveled by the car the greatest?

Example: a car traveling on a local highway

A steep slope indicates a rapid change in velocity (or speed), and thus a large acceleration.A horizontal line has zero slope and represents zero acceleration.

Horizontal axis represent time, and the vertical axis represent acceleration.

Acceleration-versus-time Graph

What can this graph tell us?

Example: 100-m Dash

What can this graph tell us?

Example (Q26 p 36).

The velocity-versus-time graph of an object is shown. Is the acceleration of the object constant?

Uniform Acceleration

Uniform Acceleration: The acceleration is constant.

It is the simplest form of acceleration.It occurs when a constant force acts on an object.Most of the examples we consider will involve

constant acceleration. Falling object. A car accelerating at a constant rate.

Uniform Acceleration (continue)

a v

t v at

v v0 at

v 1

2v 1

2at

d v t 1

2at 2Zero initial velocity

Uniform Acceleration (continue)

a v

t v at

v v0 at

Non-zero initial velocity

d v0t 1

2at 2

Example (SP2, p37)

a) What is the average acceleration between 0 s and 4 s?

b) What is the average acceleration between 4 s and 8 s?

c) What is the average acceleration between 0 s and 8 s?

d) Is the result in (c) equal to the average of the two values in (a) and (b)?

The velocity of a car increases with time as shown.