Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s. a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. d. Determine the position function s ( t ) using the Fundamental Theorem of Calculus ( Theorem 6.1 ). Check your answer by finding the position function using the antiderivative method. 3. v ( t ) = 12 t 2 − 30 t + 12 , for 0 ≤ t ≤ 3 ; s ( 0 ) = 1
Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s. a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction. b. Find the displacement over the given interval. c. Find the distance traveled over the given interval. d. Determine the position function s ( t ) using the Fundamental Theorem of Calculus ( Theorem 6.1 ). Check your answer by finding the position function using the antiderivative method. 3. v ( t ) = 12 t 2 − 30 t + 12 , for 0 ≤ t ≤ 3 ; s ( 0 ) = 1
Displacement, distance, and position Consider an object moving along a line with the following velocities and initial positions. Assume time t is measured in seconds and velocities have units of m/s.
a. Over the given interval, determine when the object is moving in the positive direction and when it is moving in the negative direction.
b. Find the displacement over the given interval.
c. Find the distance traveled over the given interval.
d. Determine the position function s(t) using the Fundamental Theorem of Calculus (Theorem 6.1). Check your answer by finding the position function using the antiderivative method.
3.
v
(
t
)
=
12
t
2
−
30
t
+
12
, for
0
≤
t
≤
3
;
s
(
0
)
=
1
An object thrown vertically upward from the surface of a celestial body at a velocity of 49 m/s reaches a height
of s= -0.7t2 + 49t meters in t seconds.
The equation of moion of a particle
CA
16
where sis
1n meters ondt io in seconds. find the velocuti nd
acceleration as functions of t. Then find the positron,
velbatr, and oceleration of the pasticle after 8
seconds.
An angler hooks a trout and reels in his line at 3 in./s. Assume the tip of the
fishing rod is 13 ft above the water and directly above the angler, and the fish is
pulled horizontally directly toward the angler (see figure). Find the horizontal
speed of the fish when it is 15 ft from the angler.
13 ft
Decreasing
at 3 in./s
Let x be the horizontal distance from the angler to the fish and z be the length of the fishing line, where both x and z
are measured in inches. Write an equation relating x and z.
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