$$
a
2
−
2
a
+
a
·
h
−
h
(
a
+
h
−
1)(
a
−
1)
(f) Calculate the limit
lim_(h->0) f(h)
=
$$
a
2
−
2
a
(
a
−
1)2
(g) A time
t>1
when the positron's instantaneous velocity is zero is
$$2
(h) Where is the positron located at the time you found in (g)
$$4
7.
12/12 points |
Previous Answers
The location
P(t)
of an object moving in the
xy
-plane at time
t
seconds is given by the equations
P(t)=
(x(t),y(t))
, where
x(t)=a +
3
t
and
y(t)=b +
4
t
,
a,b
are constants and distances are measured in units of
meters. The equations
x(t), y(t)
describe
linear parametrized motion
; see section 10.1 of the textbook
for review.
(a) The location of the object at time
t=1
is (
$$
a
+3
,
$$
b
+4

12/14/16, 4(14 PM
hw07S2.7-8
)
(b) The average rate of change of
x(t)
between 1 and 2 seconds is
$$3
m/s; this is called the average velocity of
x(t)
on the time interval [1,2].
(c) The instantaneous rate of change of
x(t)
at time
t=1
is
.

Page 9 of 12

(d) What is the instantaneous horizontal velocity of the object at time
t
?

(e) The average rate of change of
y(t)
between 1 and 2 seconds is
$$4

(f) The instantaneous rate of change of
y(t)
at time
t=1
is
.

(g) What is the instantaneous vertical velocity of the object at time
t
?

12/14/16, 4(14 PM
hw07S2.7-8
Page 10 of 12
$$
b
−
(43)
·
a
.
(i) Let
d(t)
be the distance the object has traveled after
t
seconds. The formula for
d(t)
is
$$
t
·√
42+32
.
(j) The instantaneous rate of change of
d(t)
at time
t
is
$$
√
42+32
. This is called the
speed
along the line of motion.

12/14/16, 4(14 PM
hw07S2.7-8
Page 11 of 12