11-3

III. Acceleration

A. Acceleration- change in velocity divided by the time for the change to occur (measure of how quickly velocity changes)

1. Change in speed

a. When an object in motion speeds up, its considered to be accelerating

1) Considered positive acceleration

b. Acceleration also occurs when an object slows down because the speed has changed

1) sometimes known as deceleration

2) considered negative acceleration

c. Free fall- the movement of an object toward Earth solely because of gravity.

1) The unit for velocity is meters per second (m/s)

2) The unit for acceleration then is meters per second per second (m/s2)

3) Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2

Each second an object is in free fall, its velocity increases downward by 9.8 meters per second. The change in the stone’s speed is 9.8 m/s2, the acceleration due to gravity.

What Is Acceleration?t = 0 sv = 0 m/s

t = 1 sv = 9.8 m/s

t = 2 sv = 19.6 m/s

t = 3 sv = 29.4 m/s

2. acceleration also occurs when an object is turning /changing direction

a. even if an object is traveling at a constant speed, it can still be accelerating if it is changing direction

3. Changes in speed and direction

a. Sometimes motion can have both speed and direction at the same time.

1) Passengers in a car moving along a winding road experience rapidly changing acceleration. The car can slow down going around a long winding curve.

A roller coaster produces acceleration due to changes in both speed and direction.

What Is Acceleration?

4. Constant Acceleration- a steady change in velocity

a. The velocity of an object moving in a straight line changes at a constant rate when the object is experiencing constant acceleration.

1) An airplane’s acceleration may be constant during a portion of its takeoff.

Constant acceleration during take off results in changes to an aircraft’s velocity that is in a constant direction.

What Is Acceleration?

B. Acceleration can be calculated for an object in a straight line if you know how an object’s velocity has changed during a given time period.

1. formula- acceleration = final velocity – initial velocity ÷ time

a. when an object speeds up, the final speed is always greater than the initial speed- “positive acceleration”

b. when an object slows, the final speed is less than the initial speed- “negative acceleration”

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2. units- meters per second squared (m/s2), (km/hr2), (mi/hr2), (cm/s2)

a. A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 meters per second. What is the acceleration of the ball?

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2s

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b. Calculate an airplane who’s speed changes from 40 m/s to 0 m/s in 5 seconds. What is its average acceleration?

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5s

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v=a=t=

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sm 400

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40

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C. Graphing Acceleration

1. Speed-versus-Time Graph

a. Constant acceleration is represented on a speed-time graph by a straight line

b. The slope of a line is the acceleration

c. The graph is an example of a linear graph, in which the displayed data form straight-line parts.

d. If a line slants upward, the graph shows that your speed is increasing (positive acceleration)

The skier’s acceleration is positive. The acceleration is 4 m/s2.

Graphs of Accelerated Motion

e. If a line slopes downward, its speed is decelerating (negative acceleration)

f. If there is a straight line across, there is no acceleration (the speed is constant)

The biker moves at a constant speed and then slows to a stop.

Graphs of Accelerated Motion

2. Distance-versus-time graph

a. Accelerated motion is represented by a curved line on a distance-time graph.

b. In a nonlinear graph, a curve connects the data points that are plotted

c. A curved line means the object is accelerating

1) A curved line shows that for each second you traveled a greater distance than the second before.

d. Since the line is increasing so is your speed.

A distance-time graph of accelerated motion is a curve. The data in this graph are for a ball dropped from rest toward the ground.

Graphs of Accelerated Motion

Compare the slope of the curve during the first second to the slope during the fourth second. An increasing slope means that the speed is increasing.

Graphs of Accelerated Motion

D. Instantaneous Acceleration- how fast a velocity is changing at a specific instant.

1. Acceleration is rarely constant, and motion is rarely in a straight line

a. Acceleration involves a change in velocity or direction or both, so the vector of acceleration can point in any direction.

b. The vector’s length depends on how fast velocity is changing.

c. For an object that is standing still, the acceleration vector is zero.