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.

(b) When does the car come to a stop?
at $t =$

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 ? left sum right sum is an underestimate, and is =
The ? left sum right sum is an overestimate, and is =

(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 =