Answered: The position of a particle at time t is…

The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time interval [4, 6]. Estimate the instantaneous velocity at t = 4.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter3: The Derivative

Section3.3: Rates Of Change

Problem 29E: Explain the difference between the average rate of change of y as x changes a to b, and the...

See similar textbooks

Related questions

Q: The length, width, and height of a rectangular box are measured with an error of at most 5%. Use a…

A: Differentiate diagonal and use error

Q: line with a constant acceleration of -8 ms 2. A De in the direction that the particle is initially…

Q: One side of a right triangle is measured as 9.5 inches and opposite angle equal to 26.75° with 0.25°…

A: One side of the right triangle is measured as 9.5 inches and opposite angle is equal to 26.75° with…

Q: A 13 foot ladder leaning against a wall is pulled away from the wall at a constant rate of 3ft/s and…

A: Given, A 13-foot ladder leaning against a wall is pulled away from the wall at a constant…

Q: a. Air is being pumped into a spherical ball in such a way that the volume increases at a rate of 10…

A: Given: Volume of sphere is increasing at a rate of 10 cm^3/sec.

Q: Each side of an equilateral triangle measures 3 cm, with a possible error of 0.1 cm. Using…

A: This question is taken from the differentiation in which we have to find the relative error in the…

Q: A water tank in the shape of an inverted cone is being filled up with water at a uniform rate of…

Q: Water is injected into a ball-shaped container of radius RR at a rate of 2 cm^3 per second. How fast…

A: Radius of spherical ball is R. Rate change in volume is 2 cubic centimeters. Mathematically, dVdt=2…

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: A closed rectangular box is to have an inside length of 8 meters, an inside width of 5 meters, an…

A: We need to find the material needed to make a container.

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 cube is heated in such a way that the volume increases at a rate of 1 mm/s. The rate of change of…

A: A cube is heated in way that volume increases at the rate of 1mm/s. the side of the cube is 7mm…

Q: The height and base radius of a circular cylinder are measured as 15 cm and 4 cm, respectively, with…

A: Note the formula and result . Volume of cylinder is . Suppose f and g is a differentiable function…

Q: A stone, projected vertically upward with initial velocity 112 ft/sec, moves according to s = 112t -…

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 60-kg skydiver jumps out of an airplane. What is her terminal velocity, in meters per second,…

A: Given, Mass (m) of the skydiver = 60-kg, and k = 10-kg/s

Q: A particle travels in a circle of radius 12 m at a constant speed of 21 m/s. What is the magnitude…

A: Given: A particle travels in a circle of radius 12 m at a constant speed of 21 m/s Therefore, speed…

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

Q: A tank initially holds 80 gal of a brine solution containing 1/8 lb of salt per gallon. At t=0,…

Q: Calculate the instantaneous velocity of a certain particle after 12 seconds. v=u+at

A: To find the instantaneous velocity of a particle after 12 seconds whose velocity is given

Q: An object is thrown vertically upward from a point 32 feet above the ground with an initial velocity…

Q: A 13 foot ladder is leaning against a wall. If the top of the ladder slips down the wall ata rate of…

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 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: use differentials to estimate the amount of metal in a cylindrical can that is 12cm high and 8cm in…

Q: Under certain conditions, cane sugar in water is converted into dextrose at a rate proportional to…

A: Given: when the initial time t=0 amount of the cane sugar is 75 kg, and the time t=30 minutes amount…

Q: An object is thrown upward from a height of 960ft960⁢ft with an initial velocity of…

A: The equation for the object's height 'h' at time t seconds is given by h(t)=-16t2+V0t+h0 Where V0 is…

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: A particle is moving along the curve y = x². As the particle passes through the point (1,e), its…

A: Given: A particle is moving along the curve y=x2. As the particle passes through the point (1, e),…

Q: Suppose the measurement of the side of a square is to be 30 cm with an error of 0.03 cm. Use…

A: Definition used - Error in area of the square - ∆A=2x∆x Here x is…

Q: A spherical balloon is increasing in volume at 24t Cm . How fast is the radius ст S. of the balloon…

Q: A mothball loses volume by evaporation at a rate proportional to its instantaneous area. If the…

Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

Q: A spherical snowball is melting in such a way that its diameter is decreasing at rate of 0.2 cm/min.…

Q: Use a linear approximation (or differentials) to estimate the number V100.5

A: To find 100.5Let y=xLet x=100 and ∆x=0.5⇒y=100y=10Differentiate…

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

Q: Use differentials to estimate the amount of metal in a closed cylindrical can that is 18 cm high and…

Q: The two legs of a right triangle are measured as 5 m and 12 m with a possible error in measurement…

Q: Suppose that a car accelerates at a rate of a(t) = t – 7 meters per second. Use the Fundamental…

A: ANSWER :

Q: Show that the period of motion of an undamped vibration of a mass hunging from a vertical spring is…

Q: If a ball is thrown vertically upward and with an initial velocity of 10 m/s, it’s velocity at the…

A: To find: The velocity at the highest point reached by the stone. Given: The initial velocity of the…

Q: A 30 foot ladder is resting against a vertical wall, with its other end on horizontal ground, with…

Q: Find the maximum rate of change of f(r,y) = sin(x + y) at the point (1,-1) and the direction at…

Q: The length and width of a rectangle are measured as 38 cm and 34 cm, respectively, with an error in…

Q: Air is being pumped into a spherical balloon so that its volume increases at a rate of 50 cm3/s. How…

A: Let radius of the balloon is =r and diameter =d=30 cm It is given that Volume increases at rate…

Q: Air is being pumped into a spherical balloon at rate of 5ft3/m. At what rate is the radius changing…

Q: 1. A particle moving along in a straight line with a uniform acceleration covers 72 cm displacement…

Question

100%

The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time interval [4, 6].

Estimate the instantaneous velocity at t = 4.

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

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 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

Explain the difference between the average rate of change of y as x changes a to b, and the instantaneous rate of change of y at x=a
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.
The velocity function is v(t)=−t^2+3t−2 for a particle moving along a line. Find the displacement and the distance traveled by the particle during the time interval [-1,6].
A ball is dropped on Mars where the distance traveled is s(t) = 1.9t^2 meters in t seconds. Compute the ball's average velocity over the time interval [4,8]. Estimate the instantaneous velocity at t = 4. use decimal notation. Give your answer to one decimal place.
The velocity function (in meters per second) for a particle moving along a line is given by (t)=t^3−4t^2. Find the displacement and the distance traveled by the particle during the time interval [-2,6]. (Hint: Draw a graph of the velocity function.) Your answers require that you enter the correct units.
If a ball is thrown straight up into the air with an initial velocity of 55 ft/s, it's height in feet after t second is given by y=55t-16t^2. Find the average velocity for the time period beginning when t=1 and lasting i) 0.5 seconds ii) 0.1 seconds iii) 0.01 seconds iv) Finally, based on the above results, guess what the instantaneous velocity of the ball is when t=1.
The position of a particle travelling along a horizontal line in t {seconds} is s(t)=2t^3-12t^2-126t+4meters Determine the acceleration of the particle when the velocity is 0.
A particle moves along the x axis with position measured relative to the origin and has an acceleration given by a(t) = 6t + 4 cm/s^ 2 at time t in seconds. If the particle’s initial velocity is -6 cm/sec and its initial position 9 cm right of the origin, find its velocity and position when t = 1 second.
The position of a particle travelling along a horizontal line in t seconds is s(t) = 2t^3 - 6t^2-144t + 6 meters. (a) Determine the time intervals when the object is slowing down or speeding up. (b) Determine the acceleration of the particle when the velocity is 0.
A ball is dropped on Jupiter where the distance traveled is s(t)=12.4t^2 meters in t seconds. a.) Determine the average velocity of the ball over the time interval [5,9]. b.) Find the average velocity of the ball over the time interval [5,5.0001]. c.) Estimate the instantaneous velocity of the ball at t=5.
The position of an object is given by s(t) = t^3 - (3/2)(t^2). What is the max and min velocity on the interval [0,2].
The position of a particle at time t is given by p(t)=7t^2.3-5t^1.2. Find the particle's acceleration