Suppose the position function for a free-falling object on a certain planet is given by s(1) =- 1412+vof+so. A silver coin is dropped from the top of a building that is 1,378 feet tall. Find the instantancous velocity of the coin when t=4. O -112 ft/sec O -38 ft/sec O -24 ft/sec

Q: (2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3. v' + t+ro If the…

A: This is a linear differential equation which have to be solved using integrating factor

Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 9t3 – 48t, then the…

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Q: 2) From assumption (c), the velocity (v) at time (t) of the water droplet is 3 v' + v = g. t+ro If…

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Q: 2. If the acceleration function of a certain particle is given by a(t) the velocity function…

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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: The velocity in m>s of an object moving alonga line over the time interval [0, 6] is v(t) = t2 +…

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Q: If the velocity is given by : (-t^2 i + 2t^2 j+ t^2 k) then the normal component of the acceleration…

A: Given: Velocity: vt=-t2i+2t2j+t2k. Then, v't=-2t i+4t j+2t k Find the normal component of the…

Q: A particle moves along the x-axis so that at time t 0 its velocity is given by v(t) = -3t2 - 2t +…

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Q: Please answers part c, d

A: As per norms, the first three questions are answered. The questions concern the linear approximation…

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = (10t(4 − t))/((t…

A: to find the displacement of the particle , integrate the velocity function vt therefore,…

Q: If a space shuttle's downward acceleration is given by y"(t) = –32 ft/s², find the osition function…

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Q: An object with an initial velocity of v(0) = 5 has an acceleration of a(t) = t² - 5. What is its…

A: Concept: The acceleration is given by the derivative of the velocity  That is a(t)=dv(t)dt Thus…

Q: If the position of an object is s(t) = 16 + 10.5t – 4.9t meters from zero in t seconds, then what is…

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Q: A particle moves with position function s = t4 – 4t3 20t2 + 20t, t > 0 - (a) At what time does the…

A: Given problem:- A particle moves with position function   S=t4 -4t³ - 20t² + 20t, t≥ 0   (a) At what…

Q: The acceleration function of a particle moving along a line is given by: a(t) = 4t – 2 in m/s² and…

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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. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: a car move with an initial velocity of * 50 m/s to the right, determine its position when t=15 s, if…

A: This is a problem related to newton's law of motion. Based on the general formula and concept we…

Q: Let v(t) = -13t + t² be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

A: Given velocity function, v(t)= -13t + t²

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 4t + 14 for time t > 0. If the…

A: Convert velocity into distance and time

Q: ) Suppose that the acceleration function of a particle moving along a coordinate line is a(t) = t –…

A: a)Givena(t) = t - 3Now average acceleration is given by ∫aba(t)dtb-aHere a=0 and…

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 moving along a line has position s(t) = t 4 - 18t2 m at time t seconds. At which times…

A: st=t4-18t2 Substitute 0 for s(t) into above position function. st=0t4-18t2=0t2t2-18=0t=0 or t2=18t=0…

Q: A particle is moving such that its position after t hours is s(t) =- -measured in meter. 4t +1 Find…

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Q: If the position of a particle is represented by x(t) = -t2 + 1, what is its instantaneous velocity…

A: We are given that the position of a particle is represented by x(t)=-t2+1. Now, we need to find its…

Q: b) The mass (in kg) of a product from a chemical reaction is denoted by 'y'. The dy rate at which…

A: b Separate the terms of both the variables Then let 1+y2=z2ydy=dzand 1+t2=u22tdt=2udu

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 moves along a line with acceleration 2 + 6t at time t. When t= 0, its velocity equals 3…

A: Particle acceleration velocity and position.

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: A particle moves along the x-axis with velocity given by v(t)=3t^2-6tv(t)=3t2−6t for time t\ge…

A: Answer and explanation is given below..

Q: A particle is moving along the x-axis so that at any time t > 0, its acceleration is given by the…

A: The acceleration of a particle is the rate of changing of velocity at time. When the velocity…

Q: A particle is moving along a straight line so that v ft/sec is the velocity of the particle at t…

A: Given v=t+3t2+3t+2. The objective is to find the distance traveled by the particle from the time…

Q: A particle moves along the x-axis so that at time t > 0 its velocity is given by v(t) = 3t² – 30t –…

A: topic - quadratic equations

Q: At time t 2 0, the velocity of a body moving along the s-axis is v=t2-7t+6. When is the body moving…

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Q: 6. Find where the velocity of a particle is zero if its position function is x(t)= t In t

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Q: Find an equation for the instantaneous velocity v(t) if the height of an object is defined as h(t)…

A: To find: The instantaneous velocity at any point in time. Given: The height of an object is .…

Q: A particle moves along the x axis with position measured relative to the origin and has an…

A: Consider that acceleration of object is given by at=6t+4 cm/s2, initial velocity is -6 cm/s and…

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 rocket accelerates by burning its onboard fuel, so its mass decreases with time. Suppose the…

A: you can clearly understand if you follow the below solution

Q: A body falls in a medium offering resistance proportional to the speed at any time "t". If the…

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Q: Suppose an object moves along a line at 19 m/s for 0sts2 s and at 25 m/s for 2<ts5 s. Sketch the…

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Q: A particle moves along the x-axis with velocity given by v(t) = 3t2 + 12t – 6 for timet > 0. If the…

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Q: Let v(t) = t2 – 10t be the velocity, in ft/sec, of an object at time t, in seconds. a) What is the…

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Q: A particle moving along a line has position s(t) = t4 − 18t2 m at time t seconds. At which times…

A: St=t4-18t2The particle passes through the origin when St=0t4-18t2=0t2t2-18=0t2=0   t2-18=0⇒t=0…

Q: Let v(t) = -14t + t² be the velocity, in ft/sec, of an object at time t, in %3D seconds. a) What is…

A: Solution is given below:

Q: A particle in R2 has a velocity function of v(t) = (3t²-4, 6t + 2) (given in m/s). After moving for…

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Q: Q2: If a body is moving along the coordinate line with velocity of: v(t) = sin(nt) 1-The position of…

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Q: Suppose that a particle moves along a straight line with acceleration defined by a(t)=t-3 where…

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Q: The position of a body moving along s-axis at any time 't is given by s(t) = 4t- 12t, then the…

A:

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.