2. The kinetic energy (E) of a moving object is directly proportional to the square of its velocity. A certain object traveling at a velocity of 20 m/s has kinetic energy E = 3600 Joules. b) What is the kinetic energy of that same object when it has a velocity of 50 m/s?

Q: 4. A car brakes with constant deceleration of 18 ft / s² producing skid marks that measure 306 feet…

A:

Q: in order for entrances to be accessible to all, ramps are being put in place in two different…

A:

Q: An airplane heading due east has a velocity of 200 miles per hour. A wind is blowing from the north…

A: The velocity of the plane=200 mph  The wind hits the plane in the direction of south. so, the…

Q: Can the distance traveled by a particle ever be less than its displacement? When are they equal?

A: No, the magnitude of the displacement is always less than or equal to the distance traveled.

Q: A park ranger is searching for bears in a region of the park where on average there are 12 bears per…

A: Introduction: It is given that there are 12 bears per square mile of the park. Further, the number…

Q: A ball is thrown vertically upwards with a velocity of 48 ft/s from the top of a building 35 ft…

A: Given that,

Q: How do you solve question 5?

A:

Q: The acceleration of a Maserati is proportional to the difference between 250 km/h and the velocity…

A:

Q: irectly proportional

A:

Q: Grumpy, anti-social Professor Sosa loves standing on top of a 262 ft building and tossing water bal-…

A:

Q: Find the work done by the gas with an initial volume of 3 cubic feet and a pressure of 1000 pounds…

A:

Q: The drag force (D) of an object falling through air varies directly as the square of its velocity…

A:

Q: A box weighing 50lbs falls from rest and the air resistance is proportional to his speed V and that…

A: We need to find velocity.

Q: 4. What constant acceleration is required to increase the speed of a car from 30 mi/h to 50 mi/h in…

A:

Q: The Volume (V) of a cone varies jointly as its height (h) and the square of its radius (r). Find the…

A:

Q: Question 4

A: Let a be the acceleration, v be the velocity, s be the position and t be the time of braking.

Q: 21. In basebalI, a batter stands 2 feet from home plate as a pitch is thrown with a velocity of 130…

A: Answer is mentioned below

Q: It is a fundamental law of Physics that the force the Earth exerts on an object 5) varies inversely…

A: Solving the equation provided in a) gives the value of K.

Q: A sphere is filled with air. If the volume of the sphere is decreasing at a rate of 534 cubic cm per…

A: Given

Q: A parachutist whose mass is 65 kg drops from a helicopter hovering 1500 m above the ground and falls…

A: Let y (t) be the Parachutist’s height above the ground. y (0) = 1500 m  ,  y’(0) = 0 and m y’’+ b y’…

Q: After 2 days, 10 grams of a radioactive substance is present. Three days later, 5 grams is present.…

A:

Q: The intensity of illumination at any point from a light source is proportional to the square of the…

A: Given that The intensity of illumination at any point from a light source is proportionalto the…

Q: An automobile uses gasoline at a rate of 12 kilometres per litre and has a 65 litre tank. How far…

A:

Q: The side of a cube decreases at a rate of 9 m/sec Find the rate at which the volume changes, when…

A:

Q: It is a consequence of Newton's law of gravitation that near the surface of any planet, the distance…

A: The distance of fallen rock in time t is expressed as D=ct2. Where, value of c is depend on the mass…

Q: It is known that a cable with a​ cross-sectional area of 0.80sq in. has a capacity to hold 2500 lb.…

A: Area measures the surface of a simple closed region. The units of area are the square of the units…

Q: A car travels in a straight line.  It increases its speed from 22 m/s to 28 m/s with a constant…

A: Since distance formula for constant acceleration is  v2=u2+2ax where v is final velocity, u is…

Q: If a substance decomposes at a rate proportional to the amount of the substance present, and the…

A:

Q: The intensity of illumination at any point from a light source is proportional to the square of the…

A: Let k be the coefficient of intensity of weaker light source. The intensity of the stronger light…

Q: Suppose that the magnitudes of two earthquakes differ by 1 on the Richter scale. Find the ratio of…

A: Earthquake A be the larger earthquake and earthquake B be the smaller one. The difference in the…

Q: The illumination of an object by a light source is directly proportional to the strength of the…

A: The illumination of an object by a light source is directly proportional to the strength of the…

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: It is believed that life appeared on Earth when 2 sets of proteins merged together to form the first…

A: a) Let at a intermediate time t amount of life Ct. Amount of protein A needed to form Ct amount of…

Q: A steel ball of mass 4 kg is dropped from a building. If the air resistance is equal to 0.371v, what…

A: Mass of ball m=4 kg Air Resistance =0.371v Now, the formula to find  velocity of ball at time t is:…

Q: The force of the wind blowing on a vertical surface varies jointly as the area of the surface and…

A:

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: Suppose that a motorboat is moving at 40 ft/s when its motor suddenly quits, and that 10 s later the…

A:

Q: The kinetic energy K of a mass is proportional to the square of its velocity y. If K = 12,960 joules…

A: To determine the kinetic energy.

Q: Assume the rate at which the zombies spread is jointly proportional to the number of encounters…

A: Given: Let the total number of student is 300 in the campus.

Q: Suppose that the intensity of a point light source is directly proportional to the strength of the…

A:

Q: A kite 100 ft above the ground moves horizontally at a speed of 8 ft/s. At which rate is the angle…

A: Given,  Consider the height of the lite from the ground is 100 ft. The speed is dxdt=8 ft/s. To find…

Q: When a ship is sailing, the fuel cost is proportional to the square of its speed relative to water.…

A:

Q: A 90 kg man lying on a surface of negligible friction shoves a 81 g stone away from himself, giving…

A: Explanation of the answer is as follows

Q: 4 mm/s when these three sides are 5cm, 4 cm sides x, y and z increase at 6 mm/s, 5 mm/s and Fig.…

A: we have to find rate of change of AC.

Q: How many kilometers can a train moving at an average velocity of 25 m/s southwest be displaced in 2…

A: Given, average velocity of train = 25 m/s 2 hours = 2x60x60 = 7200 seconds

Q: A car drives with velocity v(t)=2.8+/t meters per second. How far does the car drive in 8 seconds?…

A: Given data: The velocity of car is vt=2.8+t. Time taken by car is t = 8 s.

Q: When the velocity v of an object is very large, the magnitude of the force due to air resistance is…

A: Consider the provided question, Given , mass of the shell = 2 kg Acceleration due to gravity = 9.81…

Q: Consider the given isosceles triangle of base 10 inches and side lengths x inches. If is increasing…

A:

Q: When a bullet is fired into a sand bank, its retardation is assumed equal to the square root of its…

A: Given is the retardation equal to square root of velocity. WE need to find time t it will take to…

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.