The rate of a runner running the 400 meter run in 50 seconds is given by a differentiable function r(t). The table below shows the rate as measured every 5 seconds.

Time (Seconds) Rate(m/sec)

0--------------------0

5--------------------5

10-------------------7

15-------------------10

20-------------------12

25-------------------13

30-------------------11

35-------------------9

40-------------------8

45-------------------7

50-------------------6

A.) Explain why r(t) is a continuous function.

B.) Given some time (t=c) on (0,50) and using correct units, explain the meaning of

lim ((r(c)-r(t))/(c-t))

t-->c

C.) Is there some time on the interval (0,50) such that r'(t)=0? Explain.

D.) Find the average acceleration on [10,40]. Label the answer in correct units.

E.) Approximate as accurately as possible the acceleration of the runner at t=30 seconds algebraically.