A constant horizontal force of 21 N pushes a 5 kg-mass through a medium that resists its motion with 0.7 N for every m/s of speed. The initial velocity of the mass is 8 m/s in the direction opposite to the direction of the applied force. Find the velocity of the mass after 30 seconds. m/s

Q: Suppose that 2 J of work is needed to stretch a spring fromits natural length of 30 cm to a length…

A: Stretched distance = 42-30 =12  cm = 0.12 m  Let F=kx [ by Hooke's law ]  So,

Q: A 4 – foot spring measures 8 feet long after a mass weighing 8 pounds is attached to it. The medium…

A: Let the displacement be s. The spring is 4 feet and length of the spring after the mass is attached…

Q: An object is shot straight upward from sea level with an initial velocity of 400 ft/sec. a. Assuming…

A: Given:An object is shot straight upward from sea level with an initial velocity of 400…

Q: Suppose it takes a force of 30 N to hold a spring that has been stretched from its natural length of…

A: Given, F= 30 N x1= 6 cm= 0.06 m x2= 8 cm= 0.08 m

Q: A spring has a natural length of 20 cm. If a force of 25 N is required to keep it stretched to a…

A: To determine the work required to stretch the spring from 22 cm to 37 cm.

Q: A man on the edge of a platform 8 ft above the ground throws a ball vertically upwards with an…

A:

Q: How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N…

A: given How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a…

Q: A heavy-duty shock absorber is compressed 2 cm from its equilibrium position by a mass of 500 kg.…

A: Let K be spring constantThen ,Kx2x10-2=500x9.8⇒K=245000 N/m

Q: Suppose that 2J of work is needed to stretch a spring from it’s natural length of 30 cm to a length…

A: Given:The original length of the spring is 30 cm.The work done to stretch the spring from 30 cm to…

Q: A body of mass m falls from the rest in a medium offering resistance proportional to the square of…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: An object of mass 4.3 kg and volume 0.3 m3 is completely submerged in a tank of fluid with density…

A: As object is complementary submerged the volume of fluid displaced object V=0.3m3  fluid density…

Q: Find the time required by the particle in passing between points which are at distances 4 and 2…

A:

Q: determine the magnitude of the force exerted by block Y on block X during this acceleration.

A: In this question, we need to find the force exerted by block Y on block X.

Q: A shell of mass 5 kg is shot upward with an initial velocity of 250 m/sec. The magnitude of the…

A: The equilibrium of a body is considered as the state of the body when there is no force acting on a…

Q: Express the velocity and the acceleration of a moving point p(r,0)

A: We have given a curve in polar coordinate : r=1+sin(θ) with θ=t2…

Q: A boat with its load weighs 1,435 N. If the force exerted upon the boat by the motor in the…

A: F=72- 2vma = 72- 2v14359.81 dvdt=72-2v∫(146.3) dv72-2v=∫ dtt=-146.32ln(72-2v)+Cv=0 at…

Q: 9.Show that the period of motion of an undamped vibration of a mass hanging from a vertical spring…

A:

Q: A spring has a natural (unstretched) length of 1 meter. If a force of 10 newtons is required to keep…

A: Explained below

Q: A 0.25-slug mass is attached to a spring and spring is stretched 1.28 ft from its natural length.…

A: Given : A 0.25 mass slug

Q: A stream of water flowing horizontally with a speed of 15ms- gushes out of a tube of cross-sectional…

A: Given that, A stream of water flowing horizontally with speed               v=15ms-1 and area of…

Q: An object is shot straight upward from sea level with an initial velocity of 750 ft/sec. a. Assuming…

A: Initial velocity = 750 ft/sec v0=750 ft/sec The object is travelling up , so the gravitational…

Q: A force of 50 pounds stretches a spring 1 inch from its natural position. Find the work done in…

A:

Q: Find the magnitude of the horizontal and vertical components of a force of 465 newtons at a bearing…

A: The solution of above question is written in step2.

Q: A force of 10 lb is required to hold a spring stretched 4 feet beyond its natural length. How much…

A: F=10 lb  x=4 feet  F=kx  k=10/4=5/2

Q: A force with magnitude 35 N acts directly upward from the xy-plane on an object with mass 7 kg. The…

A:

Q: How much work does it take to slide a crate 20 m along a loading dock by pulling on it with a 200-N…

A: Here it is given that a force of 200N is applied at an angle of 30 degrees from horizontal to move a…

Q: Find the work done (in Joules) in pushing a car a distance of 8 meters while exerting a constant…

A:

Q: . A spring has a natural length of 40 cm. If a 60-N force is required to keep the spring compressed…

A: Given natural length of spring , l=40 cmFor a change in length , △x of 10 cm , 60 N force is…

Q: 1) What is the force on a 1000 kg elevator accelerating at 2 m/s2?

A: Force = mass * acceleration.

Q: A spring has a natural length of 10 feet, and when an 64lb weight is attached, the spring measures…

A: Consider the provided question,

Q: 7. A 16 lb weight moves in a horizontal straight line under the joint action of a constant force of…

A:

Q: A mass weighing 4 pounds is attached to a spring whose constant is 2 Ib/ft. The medium offers a…

A:

Q: A force of 200 N will stretch a garage door spring 0.8 m beyond its unstressed length. How far will…

A: Given information:

Q: It took 1800 J of work to stretch a spring from its natural length of 2 m to a length of 5 m. Find…

A:

Q: A particle of mass, m, moves along a straight line while subject to (1) a force proportional to its…

A:

Q: A force of 40 N is required to hold a spring stretched 5 cm beyond its natural length. How much work…

A:

Q: A runner starts from rest and accelerates at 2 m/s?. Assuming constant acceleration for the entire…

A: Given that a runner starts from rest and accelerates at  2 m/s2. And the acceleration is constant…

Q: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

A:

Q: It takes 1700 J of work to stretch a spring from its natural length of 1 m to a length of 6 m. Find…

A:

Q: It takes 1,600 joules (J) of work to stretch a spring from its natural length of 4 meters (m) beyond…

A: W=12kA2, where A is stretched or compressed length of spring

Q: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

A: Given: When a particle of mass m is at (x, 0), it is attracted toward the origin with a force whose…

Q: A spring is stretched 4 in. by a 2-lb weight. The 2-Ib weight is started from the equilibrium point…

A:

Q: A sky diver weighing 192 lb (including equipment) falls vertically downward from a very high…

A: Given:

Q: A wooden ball of weight 196 newtons is dropped vertically from a height of 100 meters above the…

A:

Q: It takes 1900 J of work to stretch a spring from its natural length of 1 m to a length of 4 m. Find…

A:

Q: A spring is stretched 8 feet into equilibrium by an object weighing 64 pounds, with a damping force…

A:

Q: body mass 4 kg falls(at rest) from a medium whose resisting force is numerically equal to 0.003v,…

A: Topic:- Basic maths

Q: A spring is stretched 1.5 inches by a 2-pound weight. If the weight is pulled 3 inches below the…

A: This is a problem of differential equation.

Q: A cannon is fired at an angle of 75° with the ground at an initial velocity of 250 m/s. Calculate…

A: To find the speed

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.