POSITION, VELOCITY, AND
ACCELERATION
Review- 3-C Continued
Important Terms
• Position Function gives the location of an object at time t, usually s(t),
x(t), or y(t)
• Velocity Function the rate of change (derivative) of position, usually v(t)
Velocity is positive for upward or rightward motion and negative for
downward or leftward motion.
• Acceleration Function the rate of change (derivative) of velocity, usually
a(t)
• Initial Positionstarting position (at ),
• Initial Velocity starting velocity (at ),
• Speed the absolute value of velocity
• Displacement the net change in position, (final pos. original pos.)
• Total Distance total distance traveled by the object in the time interval
(takes into account all direction changes)
3
2
s
(
t
)

16
t

36
t
 24
5) Use the position function
of an object moving on a horizontal line
a) What is the initial position of the object?
b) What is the velocity of the object at t = 1 seconds?
5)
s (t )  16t  36t  24
3
2
c) What is the speed of the object at t = 1 second?
d) What is the acceleration of the object at t = 1 second?
5)
s (t )  16t  36t  24
3
2
e) When is the object at rest?
f) When is the object moving right?
5)
s (t )  16t  36t  24
3
2
g) When is the object moving left?
h) When is the velocity of the object 54 ft/sec?
5)
s (t )  16t  36t  24
3
2
i) What is the displacement of the object between t = 0 and
t = 2 seconds?
j) What is the total distance traveled by the object between
t = 0 and t = 2 seconds?
6) The graph shows the position function of a
radio controlled model car.
a) Was the car going faster at A or B?
b) When was the car stopped?
c) At which point was the car’s velocity the greatest?
d) At which point was the cars speed the greatest?
7) Suppose a ball is thrown upward from the
top of a cliff whose
distance
is
given
by
s (t )  16t 2  48t  160
a) find the initial velocity
7) Suppose a ball is thrown upward from the
top of a cliff whose
distance
is
given
by
s (t )  16t 2  48t  160
b) At what time does the ball hit the ground?
7) Suppose a ball is thrown upward from the
top of a cliff whose
distance
is
given
by
s (t )  16t 2  48t  160
C) At what time does the ball reach its maximum
height?
HOME WORK
Worksheet 3-C on
position, velocity and
acceleration.