Interpreting the derivative Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer. 49. An object dropped from rest falls d ( t ) = 16 t 2 feet in t seconds. Find d ′(4).
Interpreting the derivative Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer. 49. An object dropped from rest falls d ( t ) = 16 t 2 feet in t seconds. Find d ′(4).
Interpreting the derivative Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer.
49. An object dropped from rest falls
d
(
t
)
=
16
t
2
feet in t seconds. Find d′(4).
Find the derivative of each function at the given point and interpret the physical meaning of this quantity. Include units in your answer Suppose the speed of a car approaching a stop sign is given byv(t) = (t - 5)2, for 0≤ t≤ 5, where t is measured in secondsand v(t) is measured in meters per second. Find v′(3).
The quantity of oxygen that can dissolve in water dependson the temperature of the water. (So thermal pollution influencesthe oxygen content of water.) The graph shows howoxygen solubility varies as a function of the water temperature T.(a) What is the meaning of the derivative S'(T) ? What areits units?(b) Estimate the value of S'(16) and interpret it.
The distance an object falls (when released from rest, under the influence of Earth's gravity, and with no air resistance) is given by
d(t)=16t2, where d is measured in feet and t is measured in seconds. A rock climber sits on a ledge on a vertical wall and carefully observes the time it takes for a small stone to fall from the ledge to the ground.
a. Compute d′(t).What units are associated with the derivative, and what does it measure?
b. If it takes 6.2s for a stone to fall to the ground, how high is the ledge? How fast is the stone moving when it strikes the ground (in miles per hour)?
Chapter 3 Solutions
MyLab Math with Pearson eText -- Standalone Access Card -- for Calculus: Early Transcendentals (3rd Edition)
Thomas' Calculus: Early Transcendentals (14th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.