# 0.11 Phy1080: motion -- variable velocity and acceleration  (Page 4/19)

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Force equals mass times acceleration

In a future module, we will learn that an object that is free to move will move and will accelerate when subjected to a force. The acceleration of the object will beproportional to the force and inversely proportional to its mass. In otherwords,

a = f/m

where

• a is the acceleration in units such as meters/sec^2
• f is force in units such as kilograms*meters/sec^2 (newtons)
• m is mass in units such as kilograms

By multiplying both sides of the equation by m, we get a more common presentation of this relationship, which is

f = m*a

where the symbols mean the same as listed above .

A ratio of two different forces of gravity

Now let's use the equation from above to form a ratio of the forces exerted on two different masses by the earth, assuming thatboth masses are the same distance from the center of the earth.

f1/f2 =(E*m1/d^2)/(E*m2/d^2)

Cancel like terms to simplify

If we cancel like terms from the numerator and denominator of the expression on the right, we can simplify the ratio to

f1/f2 = m1/m2

Replacing the forces on the left by the expression from above , we get

m1*a1/m2*a2 = m1/m2

Multiplying both sides by m2/m1 we get

a1/a2 = 1

or

a1 = a2

This shows that the acceleration resulting from the gravitational force exerted on two objects that are equally distant from the center of mass of theearth is the same regardless of the differences in mass of the two objects.

## Discussion and sample code

I will present and explain several different scenarios based on the above assumptions in this section.

## Creation of tactile graphics

The module titled Manual Creation of Tactile Graphics explained how to create tactile graphics from svg files that I will provide.

If you are going to have an assistant create tactile graphics for this module, you will need to download the file named Phy1080.zip , which contains the svg files for this module. Extract the svg files from the zip file and provide them to your assistant.

Also, if you are going to use tactile graphics, it probably won't be necessary for you to perform the graph board exercises. However, you shouldstill walk through the graph board exercises in your mind because I will often embed important physics concepts in the instructions for doing the graph boardexercises.

In each case where I am providing an svg file for the creation of tactile graphics, I will identify the name of the appropriate svg file and display animage of the contents of the file for the benefit of your assistant. As explained here , those images will be mirror images of the actual images so that your assistant can emboss the image from the back ofthe paper and you can explore it from the front.

I will also display a non-mirror-image version of the image so that your assistant can easily read the text in the image.

Also in those cases, I will provide a table of key-value pairs that explain how the Braille keys in the image relate to text or objects in the image.

## Variable velocity exercise #1

An archer that is six feet tall shoots an arrow directly upward with a velocity of 100 feet per second. Assume the arrow is at a height of 6 feet whenit leaves the bow. Also ignore the effects of air resistance.

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