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!
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!
