# Acceleration

## Acceleration


### Section Key Terms


### Defining Acceleration

Throughout this chapter we will use the following terms: time, displacement, velocity, and acceleration. Recall that each of these terms has a designated variable and SI unit of measurement as follows:
1. Time: t, measured in seconds (s)
2. Displacement: Δd, measured in meters (m)
3. Velocity: v, measured in meters per second (m/s)
4. Acceleration: a, measured in meters per second per second (m/s2, also called meters per second squared)
5. Also note the following:

Acceleration is the change in velocity divided by a period of time during which the change occurs. The SI units of velocity are m/s and the SI units for time are s, so the SI units for acceleration are m/s2. Average acceleration is given by
Average acceleration is distinguished from instantaneous acceleration, which is acceleration at a specific instant in time. The magnitude of acceleration is often not constant over time. For example, runners in a race accelerate at a greater rate in the first second of a race than during the following seconds. You do not need to know all the instantaneous accelerations at all times to calculate average acceleration. All you need to know is the change in velocity (i.e., the final velocity minus the initial velocity) and the change in time (i.e., the final time minus the initial time), as shown in the formula. A component of the average acceleration can be positive, negative, or zero. A negative acceleration component is simply an acceleration in the negative direction along that axis. When the motion is in one dimension, we often simply refer to this as negative acceleration, and acceleration in the positive direction as positive acceleration.
Keep in mind that although acceleration points in the same direction as the change in velocity, it is not always in the direction of the velocity itself. When an object slows down, its acceleration is opposite to the direction of its velocity. In everyday language, this is called deceleration; but in physics, it is acceleration—whose direction happens to be opposite that of the velocity. For now, let us assume that motion to the right along the x-axis is positive and motion to the left is negative.
 shows a car with positive acceleration in (a) and negative acceleration in (b). The arrows represent vectors showing both direction and magnitude of velocity and acceleration.
Velocity and acceleration are both vector quantities. Recall that vectors have both magnitude and direction. An object traveling at a constant speed does accelerate if it changes direction. So, turning the steering wheel of a moving car makes the car accelerate because the velocity changes direction.

### Calculating Average Acceleration

Look back at the equation for average acceleration. You can see that the calculation of average acceleration involves three values: change in time, (Δt); change in velocity, (Δv); and acceleration (a).
Change in time is often stated as a time interval, and change in velocity can often be calculated by subtracting the initial velocity from the final velocity. Average acceleration is then simply change in velocity divided by change in time. Before you begin calculating, be sure that all distances and times have been converted to meters and seconds. Look at these examples of acceleration of a subway train.
Recall that for analysis of motion in only one dimension, we do not need to use vectors. Instead, we can treat displacement, velocity, and acceleration as scalars. Unlike magnitudes, scalars can be positive or negative, so the sign can serve to tell us the direction along the one-dimensional axis.

### Practice Problems


### Check Your Understanding


### Section Summary

1. Acceleration is the rate of change of velocity. Its magnitude is expressed in units of m/s2.
2. The components of acceleration may be positive or negative.

### Key Equations


### Concept Items


### Critical Thinking


### Problems


### Test Prep Multiple Choice


### Test Prep Short Answer


### Test Prep Extended Response
