A car going at 28 \ \mathrm{ft/s} decelerates at a
constant 4 \ \mathrm{ft/s^2} to come to a stop.

**(a)**
Fill in the following table showing the velocity of the car every second.
Fill in a zero velocity for any time after that at which the
car comes to a rest.

0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | |

**(b)**
When does the car come to a stop?

at

Using your table, find left and right sums which estimate the total
distance traveled before the car comes to rest. Which is an
overestimate, and which is an underestimate?

The

The

**(c)**
On a sheet of paper, sketch a graph of velocity against time. On the
graph, show an area representing the distance traveled before the car
comes to rest. Use the graph to calculate this distance.

distance =

**(d)**
Now find a formula for the velocity of the car as a function of time:

velocity =

and then find the total distance traveled by antidifferentiation.

distance =

You can earn partial credit on this problem.