1-4 A particle moves according to a law of motion s = f(t), t> 0, where t is measured in seconds and s in feet. (a) Find the velocity at time t. (b) What is the velocity after 1 second? (c) When is the particle at rest?

Q: 7. A particle of mass m moves under gravity in a medium whose resistance is Kitimes its velocity,…

A: The equation of the motion of the particle can be written as, ma=-mg-kv So, in the differential form…

Q: 1.  A high-speed bullet train accelerates and decelerates at the rate of 10 ft/s2. Its maximum…

A: A high-speed bullet train accelerates and decelerates at the rate of 10ft/s2. Its maximum cruising…

Q: 3. Newton's Law of Cooling states that the rate of cooling of an object is proportional to the…

A: Solve these question by differentiation method.

Q: 1. (а) A spring with spring constant 12 pounds per foot is attached to the ceiling. A 4 pound weight…

A: Given Spring constant λ= 12 pounds per foot Weight w= 4 pound  Damping force Df= 2 times velocity

Q: 1. A bacteria culture starts with 1000 bacteria, and after 2 hours the population is 2500 bacteria.…

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Q: 3. A cheesecake is taken out of the oven with an internal temperature of 165 F, and is placed into a…

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Q: 1 1 A tank contains 440 gallons of water and 50 oz of salt. Water containing a salt concentration of…

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Q: 6. A car accelerates from 5 km./h. to 41 km./h. in 10 sec. . Express this acceleration in : i)km./h.…

A: Velocity and acceleration

Q: Person A runs around a circular track of radius 100m at a constant speed of 8m/s. Person B is…

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Q: 6. A car accelerates from 5 km./h. to 41 km./h. in 10 sec. . Express this acceleration in : i)km./h.…

A: We can find the acceleration by dividing the difference of final and initial velocity by total time…

Q: 4. Newton's law of cooling says that the temperature of a body changes at a rate proportional to the…

A: Given Newton's law of cooling says that the temperature of a body changes at a rate proportional to…

Q: 5. A particle, initially at rest, moves along the x-axis such that the acceleration at time t>0 is…

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Q: 7 A particle moves in a straight line and it passes through a fixed point O. Its velocity, v m s', t…

A: Given:-  V(t) = t2+kt+8 V(t) velocity in ms-1 Assume a(t) is acceleration in ms-2 To find:- (a) Find…

Q: (10) A body moves in such a way that the spaces described in the time t from starting is given by…

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Q: A particle moves along a line so that its velocity at time t is v(1) = - ? + 1+6(measured in meters…

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Q: Solve the problem in Attachment

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Q: A turkey is taken out of an oven and cools following Newton's Law of Cooling. The temperature of the…

A: The Newton's law of cooling formula can be denoted as dT/dt = -k( T - Ts), the negative sign…

Q: 1. A Boeing 747 airplane needs to be traveling at 300 km/hour to take off. The airplane spends 10…

A:

Q: 4. A cup of coffee at temperature P cools at a rate proportional to the difference between its…

A: Initial temperature of cup of coffee=P Surrounding temperature=P0 Time at which cooling start taking…

Q: In a lake, two boats A and B are leaving Station1 at the same time, Boat A is directed straight to…

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Q: 1. A stone is thrown vertically upward with a velocity of 96 ft/s from the top of a tower 112 ft…

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Q: tower stands tall at 30ft. Person A walks away from the tower at a constant rate of 3ft/s. A…

A: We will solve the problem.

Q: 16. A student constructs the apparatus below. All cha ball solid surface A ball, initially at rest,…

A: Given , Initial speed , u = 0 ( At rest )  Final speed , v = 20 m/s . Time , t = 10 seconds .

Q: 6. Solve the initial-value problem и, +ии, 3D0 with the initial curve x = - t², t= t, u = t.

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Q: EXAMPLE 2 Consider again our analysis of a heavy rock blown straight up from the ground by a…

A: Given problem:- Consider again our analysis of a heavy rock blown straight up from the ground by a…

Q: Which of the following is TRUE about differential equation? O a. Differential equation is an…

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Q: 2. A cup of tea is prepared in a preheated cup with hot water so that the temperature of both the…

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Q: (11) A particle, initially at rest, moves along the x -axis such that its acceleration at time 1>0…

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Q: A virus infects by contact and is more contagious during winter. if you are first infected, you will…

A: A virus infects by close contact, is most contagious during the winter, and everyone who becomes…

Q: 6. The pressure P, volume V, and temperature T of a sample of a certain gas follows the law: 0.25 T…

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Q: ind the third derivative of the situation stated below 1945, a narra seed was planted same as the…

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Q: 28. A particle moves along the curve y = 3x2 +1 in such a way that the y value is increasing at the…

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Q: 4 A body moves on a coordinate line such that it has a position s f(t) = 2 on the interval 1sts2,…

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Q: 2. (15 points) Identify the type of the differential equation and solve the initial value prob- lem…

A: This is linear non-homogeneous differential equation. We will solve it first get the integrating…

Q: Find the solution of the initial value problem A mass of 5 kg stretches a spring 10 cm. The mass is…

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Q: 6. Solve the initial-value problem и, +ии, 3D0 with the initial curve x = - t², t= t, u = t.

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Q: 1. The differential equation of the family of straight lines whose sum of slope and x-intercept is…

A: For X-intercept we put y=0 in y= mx+c then solve it.

Q: 2. A particle moves in a straight line and, at timet, has velocity v ms-1 with v = 4t - 12et (t 2 0)…

A: Acceleration is rate of change of velocity wrt time. Displacement is equal to velocity*time.

Q: Ordinary Differential Equations (answer included)

A: Here,weight of boat= 64,000 lbForce/thrust produced = 50,000 lb

Q: 21. A subway train travels from one station to the next in 2 min. Its distance, in kilometres, from…

A: Given the query is to find the the time when velocity will be 0.5 km/min.

Q: *12-8. A particle is moving along a straight line such that its position is defined by s = (10r² +…

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Q: Example 1: A particle moves according to the law of motion s= f (t) = 0.01r* – 0.04r² , t 2 0, where…

A: Since this question contains multiple parts and you have not specified any questions in special, I…

Q: A particle moves accroding to a law of motion s ( x ) = x 4 − 4 x 3 + 4 x 2 ,   x ≥ 0   where x is…

A: We are allowed to solve three sub-parts of a question in a session, so I will solved first three…

Q: A mass weighing 24 pounds, attached to the end of a spring, stretches it 4 inches. Initially, the…

A: Given  m=24 g=32

Q: 2- A hot-air balloon is moving vertically up and down so that its height relative to the ground is…

A: We have to find the velocity and acceleration.

Q: An analog clock with a minute hand and an hour hand is placed in the center of the XY plane. At…

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Q: Find the solution of the initial value problem A mass of 5 kg stretches a spring 10 cm. The mass is…

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Q: Part II - Obtain the differential equation of the family of curves as described. Draw some…

A: We have to find the differential equation of the parabola with axis parallel to x-axis.

Q: EXAMPLE 2 Consider again our analysis of a heavy rock blown straight up from the ground by a…

A: according to question, velocity of the rock at any time t during its motion is given by  vt=160-32t…

Q: 6. A 1kg mass is attached to a spring (with spring constant k = 4 N/m), and the spring itself is…

A: We have to find the equations of velocity acceleration . Fund when the mass comes to momentary rest,…