AccelerationAcceleration

5. The motion of a particle along a straight line is depicted in this graph.

AssessmentAssessment

V(m/s)

t (s)

What is the acceleration of the particle from 7 seconds to 10 seconds?

Velocity vs. time

a coaster making a turn

a ball rolling uphill

a baseball falling

Examples Examples An accelerating object has a changing velocity.

0 m/s 4 m/s

4 m/s 4 m/s 4 m/s 4 m/s

2 m/s

Two balls are moving to the right. Their velocity at each second is shown.

•Which ball is accelerating?

•What is its acceleration?

6 m/s

What is acceleration? What is acceleration?

0 m/s 4 m/s

4 m/s 4 m/s 4 m/s 4 m/s

2 m/s

Two balls are moving to the right. Their velocity at each second is shown.

•Which ball is accelerating?

•What is its acceleration?

Ball 2 is accelerating at +2 m/s per second:

a = +2 m/s2

6 m/s

What is acceleration? What is acceleration?

The acceleration tells you how many meters per second your velocity changes in each second.

These units are usually written as meters per second squared.

Units of acceleration Units of acceleration

Click on this interactive calculator on page 110.

Exploring the ideasExploring the ideas

Positive acceleration of +4 m/s2 adds +4 m/s of velocity each second.

Negative acceleration of -4 m/s2 adds -4 m/s of velocity each second.

0 m/s 4 m/s 8 m/s 12 m/s 16 m/s

16 m/s 4 m/s12 m/s 8 m/s 0 m/s

Signs of the acceleration Signs of the acceleration

Test your knowledgeTest your knowledge

A car is headed west (the negative direction) on a long straight road. The driver sees a red light up ahead and slows to a stop.

Is the car’s acceleration positive or negative?

Test your knowledgeTest your knowledge

A car is headed west (the negative direction) on a long straight road. The driver sees a red light up ahead and slows to a stop.

Is the car’s acceleration positive or negative?

Slowing down in the

negative direction is +a!

No acceleration

constant velocity

No acceleration

constant velocity

Positiveacceleration

changingvelocity

1. A car moves at a constant speed of 3 m/s for 3 seconds.

2. The car accelerates to 6 m/s over the next 3 seconds.

3. The car continues at 6 m/s for three more seconds. What does this look like?

Acceleration on the v vs. t graphAcceleration on the v vs. t graph

An object starting from rest accelerates at 1 m/s2.

Its velocity increases with time, making a linear v vs. t graph.

What does the position vs. time graph look like?

•As the velocity increases the slope must change!

The graph is a curve.

Position vs. timePosition vs. time

Acceleration creates a sloped line on a v vs. t graph.

Acceleration creates a curve on an x vs. t graph.

Curves vs. linesCurves vs. lines

AssessmentAssessmentA car changes its velocity from 0 to 20 m/s in 4.0 seconds. What is its acceleration?

AssessmentAssessmentA car changes its velocity from 0 to 20 m/s in 4.0 seconds. What is its acceleration?

A change of +20 m/s over 4.0 seconds is an acceleration of +5.0 m/s2.

Gravity and free fallGravity and free fall

An object is in free fall whenever it moves solely under the influence of gravity, regardless of its direction.

A ball falling down, with negligible air

resistance

What is free fall?What is free fall?

A ball thrown up, with negligible air resistance

A ball launched at ANY angle, as long as there is negligible air resistance

• after 1 second its velocity is -9.8 m/s.

• after 2 seconds its velocity is -19.6 m/s.

• after 3 seconds its velocity is -29.4 m/s.

• after 10 seconds its velocity is -98 m/s.

Gravity and free fallGravity and free fall

Near Earth’s surface, free-falling objects have a downward acceleration of 9.8 m/s2.

If an object is dropped from rest, then . . .

The only difference is that you already know the acceleration because it is always 9.8 m/s2 downward.

The free fall equations are identical to the equations for motion with constant acceleration:

Describe free fall with equationsDescribe free fall with equations

Use this equation for free fall to find your own reaction time—the time to catch a falling ruler.

Make a prediction first: Will your reaction time be in seconds? Tenths of a second? Hundredths of a second?

Find your reaction timeFind your reaction time

Do falling objects REALLY keep moving faster and faster?

No! In real life there is air resistance. As falling objects speed up, the force of air resistance increases.

When the air resistance gets as strong as the force of gravity, the falling object stops accelerating.

Gravity and free fallGravity and free fall

Most objects reach this terminal velocity within a few seconds of being dropped.

Terminal velocity is the final maximum velocity an object reaches because of air resistance.

A falling human has a terminal velocity of about 140 miles per hour (or about 60 m/s).

Terminal velocityTerminal velocity

Free fall is a very good approximation for solid, dense objects dropped from ten meters or so.

For these situations, air resistance can be ignored.

The symbol g is often used when the acceleration of an object is due only to gravity.

When can motion be treated as free fall?When can motion be treated as free fall?

Example free fall problemExample free fall problemFrom what height should you drop a ball if you want it to hit the ground in exactly 1.0 second?

Asked: x

Given: t v0

Relationship:

Solution:

Example free fall problemExample free fall problemFrom what height should you drop a ball if you want it to hit the ground in exactly 1.0 second?

Asked: x

Given: t = 1.0 s, g = -9.8 m/s2

(assume v0 = 0 m/s and x0 = 0 m)

Relationship:

Solution:

Example free fall problemExample free fall problemFrom what height should you drop a ball if you want it to hit the ground in exactly 1.0 second?

Asked: x

Given: t = 1.0 s, g = -9.8 m/s2

(assume v0 = 0 m/s and x0 = 0 m)

Relationship:

Solution:

Example free fall problemExample free fall problemFrom what height should you drop a ball if you want it to hit the ground in exactly 1.0 second?

Asked: x

Given: t = 1.0 s, g = -9.8 m/s2

(assume v0 = 0 m/s and x0 = 0 m)

Relationship:

Solution:

Asked: x

Given: t = 1.0 s, g = -9.8 m/s2

(assume v0 = 0 m/s and x0 = 0 m)

Relationship:

Solution:

The negative sign means that the final position is 4.9 m below the initial position.

4.9 mhigh

Example free fall problemExample free fall problemFrom what height should you drop a ball if you want it to hit the ground in exactly 1.0 second?

AssessmentAssessmentA ball is thrown straight upward at 15 m/s.

a) How long does it take to reach its highest point?

b) What height does it reach, assuming it started at zero height?

A ball is thrown straight upward at 15 m/s.

a) How long does it take to reach its highest point?

asked: time

given: v0 = 15 m/s, v = 0 m/s, a = g = -9.8 m/s2

relationship:

solution:

AssessmentAssessment