Answered: Suppose that the position of a particle…

Math

Calculus

Suppose that the position of a particle is given by s(t)= 2t^3+6t+9(a) Find the velocity at time t.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter2: Graphical And Tabular Analysis

Section2.1: Tables And Trends

Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...

See similar textbooks

Related questions

Q: Suppose oil spills from a ruptured tanker and spreads in a circular pattern. If the radius of the…

A: Suppose that the radius of circular pattern is “r” and area of the pattern is “A” then, The area of…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast i the…

A: We need to find the rate of change of volume of cube when side is 20 inches. Volume of cube=(side)3…

Q: Find the points where the tangent line to y =2+4 is horizontal (Critical points)

A: We need to find points where the tangent line to y=xx2+4 is horizontal. In other words, we need to…

Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

Q: A stone is thrown vertically upward with a velocity of 40 feet per second from the top of a tower…

A: Given that - A stone is thrown vertically upward with a velocity of 40 feet per second from the top…

Q: Suppose a metal rod has length 20 cm and diameter 6 cm. If it is to be insulated, except for the…

A: Let the volume of the rod be V Radius of the rod be R and length be L Given: L=20cm; R=3 cm…

Q: 3. Water is flowing out of a cylindrical storage tank at a rate of 2 m3/min. If the tank has a…

Q: A particle moves along the curve y = V1+ x3. As it reaches the point (2, 3), the y-coordinate is…

Q: Suppose that the sides of a cube are expanding at a rate of 2 inches per minute. How fast is the…

A: all details are given in below. please check it

Q: A 10-metre ladder is placed against a vertical wall. Suppose the bottom of the ladder slides away…

Q: A barge takes 3 hours to move (at a constant rate) downstream for 21 miles, helped by a current of 2…

A: To solve the following problem

Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

Q: Water is being poured at the rate of 2z m' /min into an inverted conical tank that is 12-meter deep…

A: We need to find rate of water leaking.

Q: If a cannonball is fired from a hillside 75 meters above ground with an initial velocity of 100…

A: Initial velocity = 100m/s Fired from a hillside 75 m above ground Final velocity , v = 0

Q: The length of the rectangle is increasing at a rate of 5 cm per second, and its width is decreasing…

A: Let the length be: l Let the width be: w

Q: A baseball diamond is a square whose sides are 90 ft long. Suppose that a player from asecond base…

Q: Two parallel sides of a rectangle are being lengthened at the rate of 20 mm/sec, while the other two…

A: Let the sides of rectangle be x and y since, two parallel sides are increasing at the rate of…

Q: Assume the accleration of the object is a(t) = −9.8 meters per second per second. (Neglect air…

A: When the ball will reach it's maximum height, at that point of instance the final velocity will be…

Q: A particle moves along a hyperbola xy=10. As it reaches the point (6, 4), the y- coordinate is…

Q: A man of height 1.8 m walks away from a 5-m lamppost at the speed of 1.2 m/s. Find the rate at which…

Q: A train moving with constant acceleration travels (24 m) during the (10th)s of its motion and (18 m)…

Q: 1. Imagine a person standing on the point in the plane (0,0) and starts running along a path traced…

Q: Suppose that a car skids 15 m if it is moving at 50 km/h when the brakes are applied. Assuming that…

A: Given that car skids, 15 m if it is moving at 50 km/h when the brakes are applied. That is,

Q: A parachutist of mass 52.4 kg jumps out of a stationary hot air balloon. Use the equation in photo…

A: Introduction: When an equation is given, we can determine the function value by putting different…

Q: Find the equation of a that has a y" = 4 if it has a slope of of 3 Curve Second derivative %3D at…

A: equation of the curve is given below...

Q: If an object in linear motion (but with changing velocity) covers As meters in At seconds, then its…

Q: At a certain moment, an object in linear motion has velocity 100 m/s. Estimate the distance traveled…

A: Given that: At a certain moment, an object in linear motion has velocity 100 m/s To estimate the…

Q: A ladder 3.9 m long is placed in a vertical plane which is at right angle to the vertical wall, the…

A: Given : The height of the ladder = 3.9m Let x…

Q: A rectangle is expanding such that its length is always 4 times its width. If the width is…

Q: Determine the time interval (s) when the molecule is moving to the left with increasing velocity.

Q: A certain cube with side equal to 5 inches is said to have an incremental error of 0.1 inch in its…

A: Topic :- Application of Derivative Volume of cube = (side)3

Q: b) Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75 meters.…

A: Given: Suppose a ball is thrown downward with a speed of 8 meters per second from a height of 75…

Q: A particle moves along the curve ln x2 = sq. root (y+1). As it arrives at the point (e, 3), the…

Q: Car B starts 30 miles directly east of car A and begins moving west at 90 mph. At the same moment…

A: We construct a triangle as shown below.

Q: Suppose a woman has enough “spring” in her legs to jump (on earth) from the ground to a height of…

Q: 1. Suppose the length of the diagonal of a square is increasing at the rate of 2 inches per second.…

Q: Suppose the side of a cube is decreasing at a rate of 2 feet per hour. What is the rate of change of…

A: Given: ds/dt=2 side=4ft

Q: A balloon is rising straight up from a level field, at a constant rate of 0.4 m/ sec. Just when the…

Q: The volume of a cube is increasing at the rate of 1200 cm3/min at the instant its edges are 20 cm…

A: Let the length of the sides of the cube = xAnd the volume of the cube = V = x^3

Q: How would I solve this derivative if both mass and velocity are changing

A: Derivative using product rule

Q: If a ball is thrown vertically upward with a velocity of 25 m/s, then its height after t seconds is…

Q: Find the equation of a curve in the xy-plane that passes through (1,3) and -6x(2+y) V3 – 3x2 whose…

A: The formula for the substitution method for definite integrals is given by, where g'(x) and f(x)…

Q: Suppose that a tumor in a person's body has a spherical shape and that treatment is causing the…

Q: The volume of a cube is increasing at the rate of 1200 cm³ / min at the instant its edges are 20 cm…

Q: A spherical snowball is melting so that its diameter is decreasing at rate of 0.2 cm/min. At what is…

Q: The accompanying figure shows the position versus time curve of a particle moving on a straight…

A: We will find whether the instantaneous velocity is increasing or not as following.

Q: A baseball diamond is a square with side 90ft. A batter hits the ball and runs toward first base…

Q: If a ball is thrown vertically upward with a velocity of 15 m/s, then its height after t seconds is…

Q: A 3-meter long steel pipe has its upper end leaning against a vertical wall and lower end on a level…

A: Given that, Length of pipe is 8m, lower end moving away at the rate of 2 cm/sec. we have to find how…

Question

Suppose that the position of a particle is given by s(t)= 2t^3+6t+9

(a) Find the velocity at time t.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Indefinite Integral$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
If a ball is thrown vertically upward and with an initial velocity of 10 m/s, it’s velocity at the highest point reached by the stone is?
What’s the Velocity at -2? Is the particle slowing or speeding at -2?
A particle is moving so that at any time t, its acceleration is 10t for t > or equal to 0. At the end of three seconds, the particle has moved 105 feet. What is its velocity at the end of 3 seconds?
How would I solve this derivative if both mass and velocity are changing
A particle moves on the line y = 2x + 1 in such a way that its x−coordinate changes at a constant rate of 4 units per second. A right triangle is formed by the vertical line from the particle to the x−axis, the line connecting the particle to the origin, and the x−axis. At what rate is the area of the right triangle changing when x = 4?
A lighthouse sits 1 km offshore, and its beam of light rotates counterclockwise at the constant rate of 3 full circles per minute. At what rate is the image of the beam moving down the shoreline when the image is 1 km from the spot on the shoreline nearest the lighthouse?
A spherical snowball melts in such a way that at the instant at which its radius is 2 centimeters, its volume is decreasing at 12 cubic centimeters per minute. At what rate is the radius of the snowball changing at that instant?
A ball is thrown vertically upward from the top of the Leaning Tower of Pisa190 feet high with an initial velocity of 96 feet per second. During which time period will the ball’s height exceed that of the tower?
A light is hung 6 meters above a straight horizontal path. If a man 2 meters tall is walking toward the light at the rate of 1.7 meters per second, at what rate is the tip of the man's shadow moving in meter/s per second?
Determine the time interval (s) when the molecule is moving to the left with increasing velocity.
Suppose a woman has enough “spring” in her legs to jump (on earth) from the ground to a height of 2.25 feet. If she jumps straight upward with the same initial velocity on the moon—where the surface gravitational acceleration is (approximately) 5.3 ft/s2—how high above the surface will she rise?