A particle starts out from the origin. Its velocity in miles per hour, after t hours is given by vit34 How far does t travel trom the 2nd hour through the Sth hour 1 tot9 From the 2nd hour through the 9th hour it will travel mi (Simplity your answer.)

Q: 15 ocket is being launched. After a while, it rises at a constant velocity of 10 miles per second.…

A: Let distance from the rocket to observer = z   Let AB = x BC = y The rocket is rising at a constant…

Q: 8. A boy on a bike rides north 5 miles, then turns east. If he rides 10 mi/hr., at what rate was his…

A: To find the time taken by the boy to travel the first 5 miles, use the velocity formula, v=st, where…

Q: T 69. Which is bigger, 7 or e™? Calculators have taken some of the mystery out of this…

A: (a)

Q: The formula for vertical position of a falling object is:      s(t) =  - 4.9t2 + vot + so To…

A:

Q: A ball is thrown downward with a speed of 19 ft/s from the top of a 361-foot-tall building. After t…

A: Given s(t)=-38t2-19t+361

Q: A ladder of length 15 meters is leaning against the side of a building. The foot of the ladder is…

A:

Q: The distance d (in ft) required to stop a car that was traveling at speed v (in mph) before the…

A: d=0.02v2+1.2v Where d is distance in ft and v is speed in mph  a) find distance     Here given…

Q: 0. 3 6. (in seconds) v() (in feet per second) 88 50 It takes 6 seconds for a car to stop when the…

A:

Q: A rope is attached to the bow of a sailboat coming in for the evening. Assume that the rope is drawn…

A:

Q: Car A drives west from point A at 30 kph. Another car B starting from B at the same time, drives…

A: The given data in the form of diagram is

Q: You want to travel from point A to point D at the fastest possible time. You can walk faster along…

A:

Q: 6. At noon, ship A is 150 km west of ship B. Ship A is sailing east at 35 km/h and ship B is sailing…

A:

Q: 7. At noon, ship A is 60 km west of ship B. Ship A is sailing south at 30 km/h and ship B is sailing…

A:

Q: A ball thrown in the air has a velocity of  v(t) = 94 − 32t ft/sec  at time t seconds. Find the…

A:

Q: A ball is thrown downward with a speed of 19 ft/s from the top of a 361-foot-tall building. After t…

A:

Q: (a) Find the acceleration at time t = 2 min of a helicopter whose height is s(t) = 400t – 5t³ m.…

A:

Q: If a rock is thrown upward on the planet Mars with a velocity  of 10 mys, its height (in meters)…

A: Given: The equation of height of the rock is thrown upward on the planet Mars with a velocity 10…

Q: (a) Find the acceleration at timet = 2 min of a helicopter whose height is s(t) = 300t – 213 m.…

A: If st represents the displacement function of an object then the acceleration the object is given by…

Q: Two cars are moving towards an intersection. One car is 170 meters north of the intersection and…

A:

Q: An object is dropped from a tower, 180 ft above the ground. The object's height above ground t sec…

A:

Q: (a) Different animals change from a trot to a gallop at the same Froude number, roughly 2.56. Find…

A: Follow the procedure given below.

Q: An object thrown vertically upward from the surface of a celestial body at a velocity of 14 m/s…

A:

Q: A ball is thrown downward with a speed of 8 ft/s from the top of a 68 ft tall building. After t…

A: Given is the function of distance as  and the total height of building as 68 ft. It is required to…

Q: At noon, ship A is 30 nautical miles due west of ship B. Ship A is sailing west at 21 knots and ship…

A:

Q: When an object is dropped straight down, the distance (in feet) that it travels in t seconds is…

A: Given: s(t)=-16t2 Find the velocity of the given.

Q: A ball thrown in the air has a velocity of  v(t) = 97 − 32t ft/sec at time t seconds. Find the total…

A:

Q: 2. A stone is thrown vertically into the air at an initial velocity of 96 ft/s. On Mars the height,…

A: Given:- A stone is thrown vertically into the air at an initial velocity of 96 ft/s. On Mars the…

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.3 cm/min.…

A:

Q: A 6-foot-high conical water tank is filled to the top. When a valve at the bottom of the tank is…

A: A 6-foot-high conical water tank is filled to the top, the height h, in feet, of the water in the…

Q: Two cars are moving towards an intersection. One car is 170 meters north of the intersection and…

A: Introduction: The formula of the linearization of the function y=f(x) at the point x=a is given by,…

Q: The vertical distance from the ground, in feet, of a point on a wheel as it rotates is given by…

A: to find-  Time t

Q: A bullet is fired straight up into the air. Its velocity after t seconds is given by v(t) = 9.81t +…

A:

Q: A particle that moves along a straight line has velocity v(t) = t'e-4 meters per second after t…

A:

Q: The length of a rectangle is given by 4t - 3 and its height is V2t, where t is time in seconds and…

A: Given:  The length of the rectangle is lt=4t-3 The height of the rectangle is ht=2t3

Q: Two jet aircraft are flying directly towards each other. Their speeds relative to the ground are 155…

A: Use the concept of  relative speed and solve the problem.

Q: Use the Positive functi on s(t)= -16t +v,t+s, for free-falling objects. A box is dropped from the…

A:

Q: Liquid if flowing into a conical tank (with vertext down) that has a radius two times its height. If…

A: NOTE: Refresh your page if you can't see any equations. . a radius two times its height so take…

Q: An object at the top of a building with height 120 feet is thrown upward with an initial speed of 28…

A:

Q: A ball thrown in the air has a velocity of  v(t) = 100 − 32t ft/sec  at time t seconds. Find the…

A: To find the displacement between t = 1 seconds and t = 8 seconds, we have to integrate the function…

Q: A 6 m ladder leans against a wall. The bottom of the ladder is 1 m from the wall at time t = 0 sec…

A: Base = 1m Ladder Height = 6m We have to calculate the velocity of the top of ladder at time t = 2…

Q: A person on the ground threw a ball at the rate 3 ft/s. The ball reached the peak of its trajectory…

A: Solution is here

Q: A ball is thrown downward with a speed of 14 ft/s from the top of a 196-foot-tall buil- After t…

A:

Q: Let x be the horizontal distance from Kate to the kite and z be the length of the string. Write an…

A: To find the rate at which the string from Kate’s hand is released when she has released 105 ft of…

Q: A ball weighing 0.2 pounds is thrown vertically upward. Its height after t seconds is given by…

A: Given,

Q: The formula for the power output of battery is P= VI-RI where V is the electromotive force in volts,…

A: Given power output of a battery is  P=VI-RI2

Q: Cannot solve

A:

Q: 4. Water leaks out of a tank at the rate of yt+1 gallons per minute, for 0 <t<120 minutes. At time t…

A: Given: The rate of water leaking is t+1 gallons per minute for 0≤t≤20 minutes, and amount of water…

Q: A boy released a balloon vertically in the middle of a hemispherical dome at a velocity of 5 m/s.…

A:

Q: A car starts moving at timet=0 and goes faster and faster. Its velocity is shown in the following…

A:

Q: A surveyor is walking at the rate of 4 ft/sec along the diameter of a circular courtyard. A light at…

A: Here I am attaching image so that you understand each and every step.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.