Let s(t) be a position function with velocity function v(t) = s'(t).
(a) If s(9) = 4 and , what is s(12)?
(b) If s(3) = -2 and , what is s(5)?
We know that
Plugging in the values we were given for s(9) and for the integral, we get
6 = s(12) – 4
so s(12) = 10.
A koala is climbing up and down its tree with velocity v(t) feet per minute, where positive values of v(t) indicate the koala is climbing up the tree.
At t = 0 minutes the koala is 5 feet above ground.
(a) If feet, how high is the koala after t = 4 minutes?
(b) If feet, how high is the koala at t = 7 minutes (use part (a))?
We're given that s(0) = 5 and , and asked to find s(4). Since
9 = s(4) – 5
and so s(4) = 14. This means the koala is 14 feet above ground after 4 minutes.
Since the koala is 14 feet above ground when t = 4, we know s(4) = 14.
We plug in these numbers:
At t = 7 minutes the koala is 11 feet above the ground.
A hummingbird flies away from its feeder with velocity v(t) feet per second and position s(t) feet away from its feeder.
(a) If s(4) = 5 feet and feet, find the hummingbird's distance from the feeder at time t = 0.
(b) If s(10) = 16 feet and feet, find s(5).
This problem is asking for s(0), so we plug in the numbers we're given and solve for s(0).
The hummingbird is 1 foot from the feeder when t = 0.
This is the same type of problem as (a), with different numbers.
The hummingbird is 18 feet from the feeder when t = 5.
(a) If and s(9) = -3, what is s(8)?
(b) If and s(7) = -4, what is s(3)?
(c) Given (a) and (b), what is ?
(d) Given (a) and (b), what is ?
(c) We know that
In (a) we were given that s(9) = -3, and in (b) we found that s(3) = -6.
(d) We know that
In (a) we found that s(8) = 1, and in (b) we were told that s(7) = -4. This means
(a) If s(2) = 7 and s(9) = 13, what is ?
(b) If s(2) = 13 and s(9) = 7, what is ?
(c) If s(2) = 13 and s(9) = 7 then what is ? (hint: one of the properties of integrals says how to change the limits of integration)
One of the properties of integrals lets us conclude that
Make it rain.
The who, what, where, when, and why of all your favorite quotes.
Go behind the scenes on all your favorite films.
You've been inactive for a while, logging you out in a few seconds...