0.11 Phy1080: motion -- variable velocity and acceleration  (Page 2/19)

Listings

• Listing 1 . Variable velocity exercise #1.
• Listing 2 . Variable velocity exercise #2.
• Listing 3 . Acceleration of gravity exercise #1.
• Listing 4 . Acceleration of gravity exercise #2.
• Listing 5 . Acceleration of gravity exercise #3.
• Listing 6 . Exercise to find the velocity.
• Listing 7 . Exercise to find the height.

Supplemental material

I recommend that you also study the other lessons in my extensive collection of online programming tutorials. You will find a consolidated index at www.DickBaldwin.com .

General background information

I will provide an introduction to variable velocity, acceleration, and the acceleration of gravity in thissection. I will provide exercises on those topics in the next section.

Variable velocity

What is velocity?

To review, you learned in an earlier module that velocity is the rate of change of position. Since displacement is a change in position, velocity is alsothe rate of displacement.

Uniform versus variable velocity

Previous modules have dealt exclusively with uniform velocity. However, many situations in life involve variable velocity and acceleration. For example, thesimple act of stopping an automobile at a traffic light and then resuming the trip once the light turns green involves variable velocity and acceleration.

Three equations

I will explain both of these topics in this module using three well-known physics equations that deal with the displacement of a projectile in a vacuum under the influence of gravity .

The equation that we will spend the most time on is

h = v0*t + 0.5*g*t^2

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).