2.8 Game 2302-0380 motion -- variable velocity and acceleration  (Page 2/17)

where

• h is the distance of the projectile above the surface of the earth
• v0 is the initial velocity of the projectile
• t is time in seconds
• g is the acceleration of gravity, approximately 9.8 meters per second squared, or approximately 32.2 feet per second squared at the surface of theearth. (We will also do an exercise involving the acceleration of gravity on the moon.)

(I will provide the other two equations later .)

Acceleration

Everyone is familiar with the acceleration that occurs when a motor vehicle speeds up or slows down. When the vehicle speeds up very rapidly, the positiveacceleration forces us against the back of the seat. (This involves the relationship among force, mass, and acceleration, which will be the subject of afuture module.)

If the vehicle slows down very rapidly or stops suddenly, the negative acceleration may cause us to crash into the windshield, the dashboard, or adeployed airbag.

The accelerator pedal

A common name for the pedal that causes gasoline to be fed to the engine is often called the accelerator pedal because it causes the vehicle to speed up.(However, I have never heard anyone refer to the pedal that causes the vehicle to slow down as the deceleration pedal. Instead, it is commonly called the brakepedal.)

Definitions

Displacement is a change in position.

Velocity is the rate of change of position or the rate of displacement .

Acceleration is the rate of change of velocity .

Jerk is the rate of change of acceleration (not covered in this module).

According to this author , there is no universally accepted name for the rate of change of jerk .

The algebraic sign of acceleration

When the velocity of a moving object increases, that is viewed as positive acceleration. When the velocity of the object decreases, that is viewed asnegative acceleration.

Uniform or variable acceleration

Acceleration may be uniform or variable. It is uniform only if equal changes in velocity occur in equal intervals of time.

A vector quantity

Acceleration has both direction and magnitude. Therefore, acceleration is a vector quantity.

The units for acceleration

The above definition for acceleration leads to some interesting units for acceleration. For example, consider a situation in whichthe velocity of an object changes by 5 feet/second in a one-second time interval. Writing this as an algebraic expression gives us

(5 feet/second)/second

Multiplying the numerator and the denominator of the fraction by 1/second gives us

5 feet/(second*second)

This is often written as

5 feet/second^2

which is pronounced five feet per second squared.

The acceleration of gravity

The exercises in the remainder of this module are based on the following two assumptions:

• For practical purposes, the effect of the acceleration of gravity is the same regardless of the height of an object above the surface of the earth,provided that the distance above the surface of the earth is small relative to the radius of the earth.
• In the absence of an atmosphere, all objects fall toward the earth with the same acceleration regardless of their masses.