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
A Ferris wheel at a theme park rotates in an anticlockwise direction at a constant rate. People enter the cars of the Ferris wheel from a platform which is above ground level. The Ferris wheel does not stop at any time. The Ferris wheel has 16 cars, spaced evenly around the circular structure. A spider attached itself to the point P on the side of car C when the point P was at its lowest point at time 1.00 pm. The height, h metres, of the point P above ground level, at time t hours after 1.00 pm is given by h(t)=62+60 sin(((5t-1)pi)/2) a) Write down the maximum height, in metres, of the point P above ground level. b)Write down the minimum height, in metres, of the point P above ground level. c) At what time, after 1.00 pm, does point P first return to its lowest point? d)Find the time, after 1.00 pm, when P first reaches a height of 92 metres above ground level. e)Find the number of minutes during one rotation that P is at least 92 metres above ground level.
The volume V of an ice cream cone is given by
V =
where R is the common radius of the spherical cap and the cone, and h is the height of the cone. Use linearization to estimate the change in the volume when R changes from R = 1.5 inches to R = 1.7 inches, and h changes from h = 4 inches to h = 4.1 inches. Give your
answer to two decimal places.
R
-----
h
6.20
|× in3
Velocity of a marble The position (in meters) of a marble,given an initial velocity and rolling up a long incline, is given bys = 100t/t + 1, where t is measured in seconds and s = 0 is thestarting point.a. Graph the position function.b. Find the velocity function for the marble.c. Graph the velocity function and give a description of the motion of the marble.d. At what time is the marble 80 m from its starting point?e. At what time is the velocity 50 m/s?
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