Chapter 2: Describing Movement in One Dimension, 1-D Linear Kinematics
Chapter 2: Describing Movement in One Dimension, 1-D Linear Kinematics
2.4 Acceleration
Authors: Paul Peter Urone, Roger Hinrichs
Adapted by: Rob Pryce, Alix Blacklin
Learning Objectives
By the end of this section, you will be able to:
- Define and distinguish between instantaneous and average acceleration.
- Understand the effect of accelerations in different directions.
- Calculate acceleration given initial time, initial velocity, final time, and final velocity.
In everyday conversation, to accelerate means to speed up. The accelerator in a car can in fact cause it to speed up. The greater the acceleration, the greater the change in velocity over a given time. Acceleration is defined as the rate of change of velocity.
Average acceleration can be calculated as:
[latex]\bar{a} = \frac {\Delta v}{\Delta t} = \frac {v_f-v_i}{t_f-t_i}[/latex]
where
[latex]\bar{a}[/latex] is average acceleration,
[latex]v[/latex] is velocity, and
[latex]t[/latex] is time.
(The bar over the a means ‘average’ acceleration)
Because acceleration is velocity in m/s divided by time in s, the SI units for acceleration are [latex]m/s^2[/latex], meters per second squared, or meters per second per second (m/s/s), which literally means by how many meters per second the velocity changes every second.
Recall that velocity is a vector—it has both magnitude and direction. This means that a change in velocity can be a change in magnitude (or speed), but it can also be a change in direction. For example, if a car turns a corner at constant speed, it is accelerating because its direction is changing. The quicker you turn, the greater the acceleration. So there is an acceleration when velocity changes either in magnitude (an increase or decrease in speed) or in direction, or both.
ACCELERATION AS A VECTOR
Acceleration is a vector in the same direction as the change in velocity, [latex]\Delta v[/latex]. Since velocity is a vector, it can change either in magnitude or in direction. Acceleration is therefore a change in either speed or direction, or both.
Keep in mind that although acceleration is in the direction of the change in velocity, it is not always in the direction of motion. When an object slows down, its acceleration is opposite to the direction of its motion. This is also known as deceleration.
MISCONCEPTION ALERT: DECELERATION vs. NEGATIVE ACCELERATION
Deceleration always refers to acceleration in the direction opposite to the direction of the velocity. Deceleration always reduces speed. Negative acceleration, however, is acceleration in the negative direction in the chosen coordinate system. Negative acceleration may or may not be deceleration, and deceleration may or may not be considered negative acceleration. For example, consider Figure 2.14. Read the caption for an explanation of how the direction of the acceleration relates to the direction of motion.
Instantaneous acceleration [latex]a[/latex], or the acceleration at a specific instant in time, is obtained by the sam