SECTION 11–3: ACCELERATION

OBJECTIVES

Identify changes in motion that produce acceleration.

Describe examples of constant acceleration.

Calculate the acceleration of an object.

Interpret speed-time and distance-time graphs.

Classify acceleration as positive or negative.

Describe instantaneous acceleration.

ACCELERATION

The rate at which velocity changes is called acceleration.

Acceleration can be described as changes in speed, changes in direction, or changes in both. Acceleration is a vector.

CHANGES IN SPEED

We often use the word acceleration to describe situations in which the speed of an object is increasing. This can be slightly misleading

ANY change in speed (speeding up or slowing down) is what scientists would call “acceleration.”

We can call a negative acceleration, or a slowing down effect, a “deceleration.”

Can an object have zero acceleration and still be moving?

CHANGES IN SPEED

If you are in a car that is stopped at a traffic light, you will feel a positive acceleration (speeding up) when the light turns green. When you reach a cruising speed, you will have zero acceleration. As you approach the next red light, you will experience a negative acceleration, or deceleration (slowing down).

An example of acceleration due to change in speed is free fall, the movement of an object toward Earth solely because of gravity.

The unit for acceleration is meters per second per second, or meters per second squared (m/s2).

CHANGES IN SPEED

Objects falling near Earth’s surface accelerate downward at a rate of 9.8 m/s2. Each second an object is in free fall, is velocity increases downward by 9.8 m/s.

After one second, an object falling would be moving at 9.8 m/s. At two seconds, its speed would be 19.6 m/s. At three seconds, its speed would be 29.4 m/s.

The change in the object’s speed is due directly to gravity.

CHANGES IN DIRECTION

Acceleration isn’t always the result of changes in speed. You can accelerate even if your speed is constant.

You experience this type of acceleration as you ride around a curve at the same speed.

You feel acceleration/deceleration, not speed or velocity.

CHANGES IN SPEED AND DIRECTION

You experience this type of acceleration when you ride a roller coaster. Typically your speed and direction are always changing.

You will also experience this type of acceleration when you slow down to enter a curve in your vehicle. In this case, both the speed and direction change.

CONSTANT ACCELERATION

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

Constant acceleration is a steady change in velocity. That is, the velocity of the object changes by the same amount each second.

An example of constant acceleration is illustrated by a jet airplane during takeoff.

CALCULATING ACCELERATION

Acceleration is the rate at which velocity changes.

You calculate acceleration for straight-line motion by dividing the change in velocity by the total time. If a is the acceleration, vi is the initial velocity, vf is the final velocity, and t is total time, this equation can be written as follows:

a = (vf – vi)/t

Think about how a change in either your final velocity or initial velocity would have an effect on the acceleration. Acceleration is a vector quantity.

CALCULATING ACCELERATION

A ball rolls down a ramp, starting from rest. After 2 seconds, its velocity is 6 m/s. What is the acceleration of the ball?

Initial velocity (vi) = 0 m/s (starting from rest)

Final velocity (vf) = 6 m/s

Total time (t) = 2 s

Acceleration (a) = (6 m/s – 0 m/s)/2 s = 6 m/s/2s = 3 m/s2

GRAPHS OF ACCELERATED MOTION

You can use a graph to calculate acceleration.

When using a speed-time graph, the slope of the line is acceleration.

This slope is change in speed divided by change in time.

SPEED-TIME GRAPHS

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

A linear graph is a graph in which the displayed data forms straight-line parts.

When the slope of a line is positive, the acceleration is positive. When the slope of a line is negative, the acceleration is negative.

DISTANCE-TIME GRAPHS

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

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

INSTANTANEOUS ACCELERATION

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

Instantaneous acceleration is how fast a velocity is changing at a specific instant.

An object has an instantaneous acceleration at all times, but sometimes the instantaneous acceleration is zero.

VOCABULARY

Acceleration

Free fall

Constant acceleration

Linear graph

Nonlinear graph