Question

In: Math

The speed of a runner increased steadily during the first three seconds of a race. Her...

The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds.

t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0
v (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2

Part 1 of 5

We will use either L6 or R6 for the upper and lower estimates.

Since the runner's speed is an increasing function, then  

will give the lower estimate, and

will give the upper estimate.

Solutions

Expert Solution

feel free to ask if you have any doubt and if you liked my answer please give a thumbs up

milcah answered 2 years ago
Next > < Previous

Related Solutions

The speed of a runner increased steadily during the first three seconds of a race. Her...
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. ft (smaller value) ft (larger value) t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.7 11.2 14.1 17.5 19.8 20
The speed of a runner increased steadily during the first three seconds of a race. Her...
The speed of a runner increased steadily during the first three seconds of a race. Her speed at half-second intervals is given in the table. Find lower and upper estimates for the distance that she traveled during these three seconds. t (s) 0 0.5 1.0 1.5 2.0 2.5 3.0 v (ft/s) 0 6.2 10.8 14.9 18.1 19.4 20.2
In a relay race, runner A is carrying the baton and has a speed of 2.60...
In a relay race, runner A is carrying the baton and has a speed of 2.60 m/s. When he is 25.0 m behind the starting line, runner B starts from rest and accelerates at 0.0600 m/s2. How long afterwards will A catch up with B to pass the baton to B?
A runner was tested on a treadmill. During the test, his speed x (in km/h) and...
A runner was tested on a treadmill. During the test, his speed x (in km/h) and his heart rate y were measured. The results are shown in the table. y 126 137 149 163 180 193 x 7 9 11 13 15 17 (a) Test for the significance of regression using the analysis of variance with α=0.01. Find the P-value for this test. Can you conclude that the model specifies a useful linear relationship between these two variables? We Choose...
The number of commercial airline boardings on domestic flights increased steadily during the 1990s as shown...
The number of commercial airline boardings on domestic flights increased steadily during the 1990s as shown in the table below. Let​ f(t) be the number of commercial airline boardings on domestic flights​ (in millions) for the year that is t years since 1990. Numbers of Commercial Airline Boardings on Domestic Flights f f(x) Year Number of Boardings​ (millions) 1991 452 1995 547 1997 599 1999 635 2000 666 Find an equation of f.
During a relay race, you run the first leg of the race, a distance of 1.8...
During a relay race, you run the first leg of the race, a distance of 1.8 ✕ 102 m to the north, in 22.34 s. You then run the same distance back to the south in 24.20 s in the second leg of the race. Suppose the positive y axis points to the north. (Express your answers in vector form). (a) What is your average velocity for the first leg of the relay race? vav, y = Incorrect: Your answer...
During the first half of a 3.0 mile bike race with a friend of yours, your...
During the first half of a 3.0 mile bike race with a friend of yours, your friend bikes the whole way at a constant speed of 23 mi/hr. You start from rest and accelerate constantly from the beginning. You both are neck-and-neck at the half-way point of the race. For the second half of the race, you maintain the same speed you had at the half-way point. How much faster does your friend need to bike in order to tie...
17) During the first half of a 2.0 mile bike race with a friend of yours,...
17) During the first half of a 2.0 mile bike race with a friend of yours, your friend bikes the whole way at a constant speed of 22 mi/hr. You start from rest and accelerate constantly from the beginning. You both are neck-and-neck at the half-way point of the race. What was your acceleration rate? Answer: Not yet correct, tries 1/35 Hint: What kind of diagram(s) might help you analyze this question? Do you need calculus to solve this problem?...
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds...
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is given by a(t) = 60t ft/s2 , at which time the fuel is exhausted and it becomes a freely “falling” body and falls to the ground. (a) Determine the position function s(t) for all times t > 0. (b) What is the maximum height achieved by the rocket? ( c) At what value of t does the rocket land?
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds...
A model rocket is fired vertically upward from rest. Its acceleration for the first three seconds is a(t)=96t, at which time the fuel is exhausted and it becomes a freely "falling" body. 1919 seconds later, the rocket's parachute opens, and the (downward) velocity slows linearly to −16 ft/s in 5 s. The rocket then "floats" to the ground at that rate. (a) Determine the position function s and the velocity function v(for all times t). v(t)=    if 0≤t≤3    ...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT