The position x of a bowling ball rolling on a smooth floor as a function of time t is given by: x(t)=v0t+x0 , where v0=2.5m/s and x0=−5.0m . The polynomial relationship between position and time for the bowling ball is _______________. View Available Hint(s)for Part A

exponential cubic linear inverse quadratic Previous Answers Correct A linear function is of the form y=mx+b where m and b are constants. Note that for a linear function written in this form, that is the highest power of the independent variable x in the polynomial expression for the dependent variable y is 1. In a linear function the constant m is called the slope, and the constant b is called the y -intercept. Part B Part complete Using this relationship, what is the position of the bowling ball at times t=4.0s and t=8.0s ? View Available Hint(s)for Part B

x(4.0s)=10m and x(8.0s)=20m

x(4.0s)=5.0m and x(8.0s)=15m

x(4.0s)=15m and x(8.0s)=25m

x(4.0s)=−17.5m and x(8.0s)=−37.5m

Previous Answers Correct Evaluation of a function at specific values of the independent variable provides the coordinates of specific points in a graph of the function. Part C From the coordinates obtained in Part B, find the slope of the position-time relationship for the bowling ball using the "rise over run" algortithm. View Available Hint(s)for Part C

What is the derivative with respect to time 

dx

dt

d

x

d

t

 of the bowling ball's position-time relationship 

(x(t)=

v

0

t+

x

0

(

x

(

t

)

=

v

0

t

x

0

, where 

v

0

=2.5m/s

v

0

=

2.5

m

/

s

 and 

x

0

=−5.0m)

x

0

=

−

5.0

m

)

?

−2.5m

−

2.5

m

0.0m/s

0.0

m

/

s

2.5m/s

2.5

m

/

s

−5.0m

−

5.0

m