Mrs. DiBartolo
Calculus
WHRHS
Name ________________________________________________ Date ____________
2.3 Word Problems
1. The velocity of an object in meters per second is: v(t )  36  t 2 , 0  t  6 .
a. Find the velocity and acceleration of the object when t = 3.
b. What can be said about the speed of an object when the velocity and
acceleration have opposite signs?
2. Because the moon has no atmosphere, a falling object on the moon encounters
no air resistance. In 1971, David Scott demonstrated that a feather and a
hammer fall at the same rate on the moon. The position function for each of
these objects is given by: s(t )  0.81t 2  2 where s(t) is the height in meters
and t is the time in seconds.
a. What is the ratio of the earth’s gravitational force to the moon’s? (In
other words, what is the ratio of the acceleration due to gravity on earth
to the acceleration due to gravity on the moon.)
3. An astronaut standing on the moon throws a rock into the air. The height of the
27
rock is given by s   t 2  27t  6 where s is measured in feet and t is measured
10
in seconds.
a. Find the equations for the velocity and acceleration of the rock.
b. Find the time when the rock is at its highest point.
c. What is the height of the rock at the time you found for part b.