A car going at 24 ft/s decelerates at a constant 4ft/s^2 to cometo a stop.
a) Fill in the following table showing the velocity of the carevery second. Fill in a zero velocity for any time after that atwhich the car comes to a rest.
| t = | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| v = | 24 | 20 | 16 | 12 | 8 | 4 | 0 | 0 |
b) When does the car come to a stop?
at t = ___6___
Using your table, find left and right sums which estimate thetotal distance traveled before the car comes to rest. Which is anoverestimate, and which is an underestimate?
The __right sum__ is an underestimate, and is = __60__
The __left sum__ is an overestimate, and is = __84__
c) On a sheet of paper, sketch a graph of velocity against time.On the graph, show an area representing the distance traveledbefore the car comes to rest. Use the graph to calculate thisdistance.
distance = ___?___
d) Now find a formula for the velocity of the car as a functionof time:
velocity = ___?___
and then find the total distance traveled byantidifferentiation.
distance = ___?___
