Measurement and Motion

Acceleration

A Model for Accelerated Motion

Free Fall and the Acceleration due to Gravity

Acceleration in a Straight Line

Objectives1. Calculate acceleration from the change is

speed and the change in time.2. Give an example of motion with constant

acceleration.3. Determine acceleration from the slope of the

speed versus time graph.4. Calculate time, distance, acceleration or

speed when given three of the four variables.5. Solve two-step accelerated motion problems.6. Calculate height, speed, or time of flight in

free fall problems.7. Explain how air resistance makes objects of

different masses fall with different accelerations.

Vocabulary Terms

acceleration m/sec2

delta constant

acceleration uniform

acceleration slope term

initial speed free fall acceleration due to

gravity (g) time of flight friction air resistance terminal speed

Acceleration

Key Question:

How is the speed of the ball changing?

Acceleration of a car

Acceleration is the rate of change in the speed of an object.

Acceleration vs. Speed

Positive acceleration and positive speed

Acceleration vs. Speed

Negative acceleration and positive speed

Acceleration

a = v t

Change in speed (m/sec)

Change in time (sec)

Acceleration (m/sec2)

Calculate Acceleration

A student conducts an acceleration experiment

by coasting a bicycle down a steep hill.

The student records the speed of the bicycle every second for five seconds.

Calculate the acceleration of the bicycle.

Acceleration and Speed Constant acceleration is different from

constant speed. Motion with zero acceleration appears as a

straight horizontal line on a speed versus time graph.

zero acceleration constant speed

Acceleration and Speed Constant acceleration is sometimes called

uniform acceleration. A ball rolling down a straight ramp has

constant acceleration.

constant acceleration increasing speed

Acceleration and Speed An object can have acceleration, but no

speed. Consider a ball rolling up a ramp. As the ball slows down, eventually its speed

becomes zero.

constant negative acceleration decreasing speed

Slope and Acceleration Use slope to recognize when

there is acceleration in speed vs. time graphs.

— Level sections (A) on the graph show an acceleration of zero.

— The highest acceleration (B) is the steepest slope on the graph.

— Sections that slope down (C) show negative acceleration (slowing down).

A Model for Accelerated MotionKey Question:

How do we describe and predict accelerated motion?

*Students read Section 4.2 AFTER Investigation 4.2

Slope of a graph

The slope of a graph is equal to the ratio of rise to run.

On the speed versus time graph, the rise and run have special meanings, as they did for the distance versus time graph.

The rise is the amount the speed changes.

The run is the amount the time changes.

Acceleration and slope Acceleration is the change in speed over the change in time. The slope of the speed versus time graph is the acceleration.

Calculate acceleration

The following graph shows the speed of a bicyclist going over a hill.

Calculate the maximum acceleration of the cyclist and say when in the trip it occurred.

Solving Motion Problems

Solving Motion Problems

Calculate speed

A ball rolls at 2 m/sec onto a ramp.

The angle of the ramp creates an acceleration of 0.75 m/sec2.

Calculate the speed of the ball 10 seconds after it reaches the ramp.

Solving Motion Problems

initial positiondistance if at constant speed

distance to add or subtract, depending on acceleration

Calculate position

A ball traveling at 2 m/sec rolls onto a ramp that tilts upward.

The angle of the ramp creates an acceleration of -0.5 m/sec2.

How far up the ramp does the ball get at its highest point?

(HINT: The ball keeps rolling upward until its speed is zero.)

Solving Motion Problems

Calculate time

A car at rest accelerates at 6 m/sec2. How long does it take to travel 440

meters (about a quarter-mile) and how fast is the car going at the end?

Calculate position

A ball starts to roll down a ramp with zero initial speed.

After one second, the speed of the ball is 2 m/sec.

How long does the ramp need to be so that the ball can roll for 3 seconds before reaching the end?

Solving Problems with Free Fall

Calculate height

A stone is dropped down a well and it takes 1.6 seconds to reach the bottom.

How deep is the well? You may assume the

initial speed of the stone is zero.

Air Resistance and Mass

The acceleration due to gravity does not depend on the mass of the object which is falling.

Air creates friction that resists the motion of objects moving through it.

All of the formulas and examples discussed in this section are exact only in a vacuum (no air).

Terminal Speed You may safely assume that a = g

= 9.8 m/sec2 for speeds up to several meters per second.

The resistance from air friction increases as a falling object’s speed increases.

Eventually, the rate of acceleration is reduced to zero and the object falls with constant speed.

The maximum speed at which an object falls when limited by air friction is called the terminal speed.

Free Fall and Acceleration due to Gravity

Key Question:

How do you measure the acceleration of a falling object?

*Students read Section 4.3 BEFORE Investigation 4.3

Application: Antilock Brakes