Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 16 lb stretches a certain spring ​9 in., how much will a force of 48 lb stretch the​ spring?

Q: ​Hooke's law for an elastic spring states that the distance a spring stretches varies directly as…

A:

Q: For a moving object, the force acting on the object varies directly with the object's acceleration.…

A: givenforce varies directly with accelerationF α aF= forcea= acceleration

Q: The sides of an equilateral triangle are increasing at the rate of 3 cm/min. Find: a) the rate of…

A:

Q: newton's law of cooling

A: We have given that a cup of hot cocoa coo from 90∘C to 60∘C after 10min in a room temperature having…

Q: Hooke’s law states that the distance that a spring is stretched by hangingobject varies directly as…

A: Let distance= y Mass of the object= x According to the question y=kx  k=constant  Given that y=20…

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -155 feet per…

A: We will find out the required value.

Q: 25. A rope is attached to a weight and passes over a hook that is 6 ft. above the ground. The rope…

A: The following diagram shows the given situation: In the above diagram, the length of the thread…

Q: 10. A ladder 15 m long leans against the wall. The ladder slides down the wall at a rate of 1.5 m/s.…

A: Here we use the property of right angle triangle.

Q: 1. A rocket is being launched vertically over a point A on the ground with a velocity of 550 mi/hr.…

A: Given:  dh / dt = 550

Q: When a constant force is applied to an object, the acceleration of the object varies inversely with…

A: let force is F apply newtons low force = mass * acceleration  detailed solution is given below

Q: ​Hooke's law for an elastic spring states that the distance a spring stretches varies directly as…

A:

Q: Newton's Law of Gravitation says that the magnitude F of the force exerted by a body f constant mass…

A:

Q: For a moving object, the force acting on the object varies directly with the object's acceleration.…

A:

Q: 3.7 - related rates car traveling north at 40 mi/hr and a truck traveling east at 30 mi/hr leave an…

A: We have given,Speed of car travelling north = 40 miles/hrSpeed of truck travelling east = 30…

Q: ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: This question is about traingles.  How we can find rate of change of angle with use of pythagorean…

Q: 1. A railway truck of mass 300 kg is travelling at a speed of 7 m/s, It collides with a second…

A: Solution

Q: 6. The angle of elevation of the sun is decreasing ata rate of 0.15 rad/h. Hbw fast is the shadow…

A: From the given data:

Q: A baseball diamond has the shape of a square with sides 90 feet long. (a) A player is running from…

A: Given a) Sides (length) of the square =90 ft Speed of the player (from first base to second base)=25…

Q: Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the…

A:

Q: 4.A ladder 10ft. long is resting against the side of a building if the foot of the ladder slips away…

A: This question is based on application of Derivative.

Q: 2. According to Newton's cooling law, the rate of cooling of a hot body is pro- portional to the…

A: This question is from Newton's law of cooling

Q: For a moving object the force acting on the object varies directly with the objects acceleration.…

A:

Q: A right triangle with legs of lengths x and y has its area given by the following. A = 1/2xy If the…

A:

Q: For a moving object, the force acting on the object varies directly with the object's acceleration.…

A: Let,Initial Acceleration, a1 = 1M/S2Initail Force, F1 = 14 NFinal Acceleration, a2 = 5 M/S2We have…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A: Given that  Height of ladder=10 ft Let θ be the angle between the ladder and ground. Then cosθ=x10…

Q: A ladder 13 m long leans against a wall. The foot of the ladder is parallel along the ground away…

A:

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A car travels along a straight line at a constant speed of E60.0mi/h for a distance d and then…

A:

Q: A train is moving due west at a constant speed. A passenger notes that it takes 10 minutes to travel…

A:

Q: A stone is dropped from the edge of a roof, and hits the ground with a velocity of -115 feet per…

A:

Q: Two roads AB and BC intersect at B, where ZABC = 60° and AB = 28 meter. A cyclist starts from A and…

A: Given, ∠ABC= 60°AB¯ = 28

Q: In Ohm's law, voltage varies directly with current. Graph and upload the direct variation…

A: The solution is :

Q: b. One airplane is approaching an airport from the north at 206 km/hr. A second airplane approaches…

A:

Q: A man 6 feet tall walks at a rate 3 feet per second away from a light that is 15 feet above the…

A: According to question Let x be the distance between lamp post and man at any instant of time "t"y…

Q: The strength of magnetic force varies inversely with the square of the distance between th magnets.…

A: Given: , Where the radius r = 5 cm, Force F=3N. To find the work required to move the magnets from a…

Q: Find a linear speed of a tip of minute hand if a length of the minute hand is 28 cm long. Hint: ()…

A: We need to find linear speed of tip of a minute hand, if the length of the minute hand is 28cm. We…

Q: Blkers A and Bare travellng on perpendicular roads. At the same time, biker A Is leaving the…

A:

Q: 4. According to Newton’s law of cooling, the rate at which a body cools is proportional to the…

A:

Q: 12. A baseball player is running from the second based to the third base at 20 ft./s. At what rate…

A:

Q: A ball is launched into the air. 21 feet away from the launch site is a camera. If the ball is…

A: We have to find the rate of change of angle of elevation as seen by a camera placed at 21 feet away…

Q: 3. According to Newton's cooling law, the rate of cooling of a hot body is pro- portional to the…

A:

Q: A man 6 feet tall walks at a rate 3 feet per second away from a light that is 15 feet above the…

A:

Q: 3) One airplane is approaching an airport from the north at 163 km/hr. A second airplane approaches…

A:

Q: A boat with its load weighs 1,500 N. If the force exerted upon the boat by the motor in the…

A:

Q: By Newton's Law of Cooling, the rate at which an object cools is directly proportional to the…

A: let T denote the temperature of an object and T0 the surrounding temperature. If t denotes time,…

Q: The volume of a sphere is changing at a constant rate. Show that the surface area changes at a rate…

A: Let, V=volume S= surface area r= radius t= time Given that dV/dt=k (constant) Differentiate both…

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the…

A:

Q: A right triangle with legs of lengths x and y has its area given by the following. If the rate of…

A: Area of a right triangle is given by A = 12xy Rate of change of x is 2 units per minute i.e., dxdt =…

Q: According to Newton's law of cooling/warming, the rate at which the temperature of a body changes is…

A: Find your answer below

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.