216 Chapter 8 Time and Time-Related Parameters

Velocity

Normal

acceleration

Normal

acceleration

Velocity

■Figure 8.8

The acceleration of a car moving

at a constant speed following a

circular path.

Linear Accelerations

Acceleration provides a measure of how velocity changes with time. Something that moves with

a constant velocity has a zero acceleration.Because velocity is a vector quantity and has both magni-

tude and direction, any change in either the direction or the magnitude of velocity can create accelera-

tion.For example, a car moving at a constant speed following a circular path has an acceleration

component due to the change in the direction of the velocity vector, as shown in Figure 8.8. Here,

let us focus on an object moving along a straight line. The average acceleration is defined as

(8.9)

Again note that acceleration uses only the dimensions of length and time. Acceleration repre-

sents the rate at which the velocity of a moving object changes with time. Therefore, accel-

eration is the time rate of change of velocity. The SI unit for acceleration is m/s

2

and in U.S.

Customary units ft /s

2

.

The difference between instantaneous acceleration and average acceleration is similar to the

difference between instantaneous velocity and average velocity. The instantaneous acceleration

can be obtained from Equation (8.9) by making the time interval smaller and smaller. That is to

say, instantaneous acceleration shows how the velocity of a moving object changes at any instant.

Let us now turn our attention to acceleration due to gravity. Acceleration due to gravity

plays an important role in our everyday lives in the weight of objects and in the design of pro-

jectiles. What happens when you let go of an object in your hand? It falls to the ground. Sir Isaac

Newton discovered that two masses attract each other according to

(8.10)

whereFis the attractive force between the masses (N),Grepresents the universal gravitational

attraction and is equal to 6.7  10

 11

m

3

/kg s

2

,m 1 andm 2 are the mass of each particle (kg),

andrdenotes the distance between the center of each particle. Using Equation (8.10), we can

determine the weight of an object having a massm(on earth) by substitutingmform 1 , substituting

form 2 the mass of the earth, and using the radius of the earth as the distancerbetween the cen-

ter ofm 1 andm 2. At the surface of the earth, the attractive forceFis called theweightof an object,

F

Gm 1 m 2

r

2

average acceleration

change in velocity

time

Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).

圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀