# The Runner's Rate

#### Mooch22

##### New member
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) :arrow: Rate (m/sec)
0 :arrow: 0
5 :arrow: 5
10 :arrow: 7
15 :arrow: 10
20 :arrow: 12
25 :arrow: 13
30 :arrow: 11
35 :arrow: 9
40 :arrow: 8
45 :arrow: 7
50 :arrow: 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 your answer correctly!

E.) Approximate as accurately as possible the acceleration of the runner at t=30 seconds. Show your work and label your answer!

#### pka

##### Elite Member
You need to tell us what you have done.
Where are you having trouble?
Because we do not do homework for you, we need to know where you are in your own work.