10. The motion of a particle is described by the position function s(t) = 2t² – 15t² +33t+17, t>0, where ț is measured in seconds and s(t) in meters.a. When is the particle at rest?b. When is the velocity positive? -c. Draw a diagram to illustrate the motion of the particle in the first 10 seconds.11. A snowball melts so that its surface area decreases at a rate of 0.5 cm?/min. Find the rateat which the radius decreases when the radius is 4 cm. (SA=4ar?)-12. Brent is driving west at 60 km/h and Aaron is driving south at 70 km/h. Both cars areapproaching the intersection of the two roads. At what rate is the distance between thecars decreasing when Brent's car is 0.4 km and Aaron's is 0.3 km from the intersection?-13. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2m³/min. Find the rate at which the water level is rising when there is 8T m³ of water.14. For the function f(x)= ax? + bx? – 5x + 9, determine the values of a and b so that f (-1)= 12 and f (-1) =3.415. Determine the equations of two lines that pass through the point (-1, -3) and are tangentto the graph of y=x² + 1+16. Two particles have positions at time t given by s1 = 4t – t'and s2 = 5t2 – t3 . Find thevelocities V and V2at the instant the accelerations of the two particles are equal.e 6. Give one example of a rate that is decreasing and one example of a rate that is increasing.7. When a vehicle is said to be travelling at -35 km/h, what does this infer?dv8. If V represents the volume of an object, what doesrepresent? e9. A construction worker accidently drops a hammer from a height of 90 m while workingon the roof of a new apartment building. The height, s, in meters, of the hammer after tseconds can be modelled by the function s(t)=90-4.0t?,t > 0.a. Determine the velocity at 1 s and 4 s. eb. When will the hammer hit the ground? ec. Determine the impact velocity of the hammer.

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Description: 10. The motion of a particle is described by the position function s(t) = 2t² – 15t² +33t+17, t>0, where ț is measured in seconds and s(t) in meters.a. When is the particle at rest?b. When is the velocity positive? -c. Draw a diagram to illustrate t

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6. Give one example of a rate that is decreasing and one example of a rate that is increasing.

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

Topic Video

Question

10. The motion of a particle is described by the position function s(t) = 2t² – 15t² +
33t+17, t>0, where ț is measured in seconds and s(t) in meters.
a. When is the particle at rest?
b. When is the velocity positive? -
c. Draw a diagram to illustrate the motion of the particle in the first 10 seconds.
11. A snowball melts so that its surface area decreases at a rate of 0.5 cm?/min. Find the rate
at which the radius decreases when the radius is 4 cm. (SA=4ar?)-
12. Brent is driving west at 60 km/h and Aaron is driving south at 70 km/h. Both cars are
approaching the intersection of the two roads. At what rate is the distance between the
cars decreasing when Brent's car is 0.4 km and Aaron's is 0.3 km from the intersection?-
13. A water tank at a filtration plant is built in the shape of an inverted cone with height 5.2
m and diameter 5 m at the top. Water is being pumped into the tank at a rate of 1.2
m³/min. Find the rate at which the water level is rising when there is 8T m³ of water.
14. For the function f(x)= ax? + bx? – 5x + 9, determine the values of a and b so that f (-1)
= 12 and f (-1) =3.4
15. Determine the equations of two lines that pass through the point (-1, -3) and are tangent
to the graph of y=x² + 1+
16. Two particles have positions at time t given by s1 = 4t – t'and s2 = 5t2 – t3 . Find the
velocities V and V2at the instant the accelerations of the two particles are equal.e

6. Give one example of a rate that is decreasing and one example of a rate that is increasing.
7. When a vehicle is said to be travelling at -35 km/h, what does this infer?
dv
8. If V represents the volume of an object, what does
represent? e
9. A construction worker accidently drops a hammer from a height of 90 m while working
on the roof of a new apartment building. The height, s, in meters, of the hammer after t
seconds can be modelled by the function s(t)=90-4.0t?,t > 0.
a. Determine the velocity at 1 s and 4 s. e
b. When will the hammer hit the ground? e
c. Determine the impact velocity of the hammer.

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