Find the position function x(t) of a moving particle with the given acceleration a(t), initial position xo =x(0), and initial velocity %3D Vo =v(0). a(t) = 4(t+ 3), v(0) = - 4, x(0) = 4 YEVRS

Q: A particle is moving with acceleration a ( t ) = 30t + 16 . its position at time t = 0 is s ( 0 ) =…

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Q: Suppose that a car gradually speeds up so that for the first 10s its acceleration is given by dv…

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Q: The equation dx/dt = kx is both separable .4 and linear اخترأحد الخيارات

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Q: 3. Find the position function x(t) given the acceleration a(t), the initial velocity vo = %3D v(0),…

A: It is given that the acceleration function is at=6t+4. The initial velocity at t=0 is v0=v0 and the…

Q: A particle moves along the x-axis with acceleration at any given time t as a(t) = 3t+4t+6,jf the…

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Q: A 100 gal-tank initially contains 50 gal of fresh water. At t = 0, a salt solution containing 1 Ib…

A: Given: A 100 gal-tank initially contains 50 gal of fresh water. At t=0, a salt solution containing 1…

Q: Apply classical fourth-order Runge-Kutta method to solve dy dx f(x,y) == 4e®** –0.3y , using h=0.5…

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Q: With what initial velocity v0 must we fire a rocket so it attains a maximum height r above the…

A: We will use the maximum height formula Where u=initial velocity. g=gravity H_max= maximum height

Q: The temperature at a point on a metal surface is T (x, y. z) = 0.05x² – 0.01y³ – z in degrees…

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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: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

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Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

A: at=4t,  v0=9,  x0=0 Integrating with respect to t, we get vt=∫at dt=∫4t dt=4·t22+C=2t2+C    →1 Put…

Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t − 3 m/s over…

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Q: Given the acceleration a=d^2s/dt^ 2​, initial​ velocity, and initial position of a body moving on a…

A: Given :- a=-81sin9t, v(0)=9,  s(0)=-7 Here, a is accelerationdvdt, v is velocity dsdt and s is…

Q: 6) A weight oscillates in a vertical motion according to the position function y(f) = -5 cos t.…

A: Acceleration for position function yt=-5cost is d2ydt2. Calculate double derivative d2ydt2 and…

Q: A particle moves along a coordinate line in such a way that its velocity at any time t is given by…

A: We have, a particle moves along a co-ordinate line in such a way that its velocity at any time t is…

Q: A parachutist of mass m falls from rest in the Earth's gravitational field and is subjected to mg…

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Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

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Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

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Q: Two particles have positions at time t given by s =4t-t^2 and s=5^2-t^3. Find the velocities v1 and…

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Q: A particle is moving with acceleration a(t) = 24t + 14. its position at time t = 0 is s(0) = 10 and…

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Q: Find all solutions of the equation: dy​/dt=yt−y−t+1. Stationary and non stationary

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Q: A spring with constant k = 7 N/m hanging from the ceiling is placed at its lower end with an object…

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Q: A particle is moving with acceleration a(t) = 36t + 18. its position at time t = 0 is s(0) = 1 and…

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Q: A particle is moving with acceleration a(t)=12·t+3. At time t=0, its position is s(0)=7 and its…

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Q: A particle is moving with acceleration a(t)=24t +14. Its position at time t=0 s(0)=11 and its…

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Q: A skydiver’s vertical velocity is governed by m(dv/dt)=mg-k(V^2) where, ? is the mass of the…

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Q: Determine the position function if the acceleration function is a(t) = 3 sint + 1, the initial %3D…

A: We have acceleration  a(t) = 3sint+1

Q: A particle is moving with acceleration a(t) = 36t + 2. its position at time t = 0 is s(0) = 2 and…

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Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: A 2-lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

A: A 2‐lb object, that stretches a spring by 1.5 inches, is released with a downward velocity of 32…

Q: A particle moves along the x-axis so that at time t >0 its position is given by x (t) =t² – 10t +…

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Q: A particle is thrown vertically upwards in the air. The distance it covers in time t is given by…

A: We will be using the fact that rate of change in distance is called velocity. v(t)=dsdt

Q: Find the position of a body moving on a coordinate line at time t for an acceleration a= dt² initial…

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Q: Find the position function x(t) of a moving particle with the given acceleration a(t), initial…

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Q: A particle moves along a straight line with velocity function v(t) = 8sin (t)- 4cos(t) and its…

A: Just integrate the velocity function and find the value of integration constant with the given…

Q: A particle is moving with acceleration a(t) = 18t + 10. its position at time t = 0 is s(0) = 11 and…

A: Given :                 at=18t +10at t=0 is  s0 = 11at t=0 is v0 =11 To find : Position at time t=6…

Q: An observer moves so that his position, velocity, and acceleration at time t are given by the…

A: Given:r(t)=x(t)i+y(t)j+z(t)kv(t)=dr/dta(t)=dv/dt

Q: An object of mass m falling near the surface of the earth is retarded by air resistance proportional…

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Q: Find an integrating factor as a function of z = x ^ 2 + y ^ 2 for the following equation and then…

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Q: A 0.5 kg mass is attached to a spring having a spring constant of 8 N/m. The mass is set into motion…

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Q: dx 2x - y dt dy

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Q: A particle is moving with acceleration a(t)=30t +18. Its position at time t=0 s(0)=11 and its…

A: Explanation of the answer is as follows

Q: 1 = x1+2y v= xt - yt w = 0 Given: What is the acceleration at a point x=1 m, y=2 m, and at a time…

A: Acceleration of particle at any point is equals to rate of change of velocity with respect to time…

Q: 1. A particle moves along the x-axis according to the equation x=2r+3F, where x is in m and is in…

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Q: 11. Find the position r(t) of an object if the acceleration is a(t) = and the initial position is…

A: We have to find out r vector

Q: A particle is moving with acceleration a(t) = 30t + 10. its position at time t = 0 is s(0) = 13 and…

A: To find out the position of the particle at t=3

Q: A spring is stretched 12 inches by a 24-pound weight. If the weight is pulled 10 inches below the…

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Q: Verify the Pierre-Simon Laplace equation ∂2f/∂x2+∂2f/∂y2=0 with f(x,y)=ln∣x2+y2∣

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