Question

instructions
look at the graphs from
the collected data.
compare them to the
graphs below. describe the
relationship between the
mass of the object and how
far the cup was pushed.
describe the relationship
between the velocity of the
object and how far the cup
was pushed.
hint?

graphs
linear
inverse linear
negative linear
squared
inverse squared
square root

answer
graph
distance cup pushed vs.
mass
distance cup pushed vs.
velocity
relationship
square root
no relationship
equation
$y=x$
none

question

1. if you wanted to push the cup farther,

would it be more efficient to increase the
mass or the velocity of the object hitting
it? explain your answer.
answer

Explanation:

1. First, refer to the established relationships: distance vs. mass has a square root relationship, while distance vs. velocity has no relationship as stated in the table.
2. A square root relationship means increasing mass will increase distance pushed, but the gain in distance slows down as mass increases. A no relationship means changing velocity does not change how far the cup is pushed at all.
3. To push the cup farther, only increasing mass will have a positive effect on the distance the cup is pushed; changing velocity will not help.

Answer:

It is more efficient to increase the mass of the object hitting it. The data shows there is a square root relationship between the mass of the object and the distance the cup is pushed, so increasing mass will make the cup go farther. In contrast, there is no relationship between velocity and the distance the cup is pushed, so changing velocity will not affect how far the cup moves.