d?s Solve dt? ds +13s = 0 , where s is the displacement of an object at time t given dt ds that s = 2, =3 when t = 0. dt

Q: 12. The velocity of a particle at time t is given by the function v(t) = t³ – sint + 2, what is the…

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Q: A particle is moving with acceleration a(t) = 18t + 6. its position at time t = 0 is s(0) = 1 and…

A: Acceleration of the particle is, at=18t+6 To find velocity function, integrate acceleration function…

Q: A particle moves on a straight line and has acceleration a(t) = 24t+2 Its position at t=0 is s(0) =…

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Q: d'x dx Solve the equation + 2x = e given that x (0) = 0, x' (0) =1. +3 dr dt %3D

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Q: ds The position of a particle at time t is given by s. Find the velocity dt 4 - 5st + 2t - 7t= 0

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Q: A particle moves along the x-axis so that its velocity r at time f'is given by v(t)=(21-3)(r² –31)…

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Q: A particle is moving with acceleration = 6t + 12. its position at time t = 0 is a(t) s(0) = 5 and…

A: First use the integration to find the velocity then again integrate to get the position function.

Q: A particle moves in a straight line with the given velocity v(t) = 4t-2 – 1 (in m/s). Find the…

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Q: A particle is moving with acceleration a(t) = 18t + 6. its position at time t = 0 is s(0) = 15 and…

A: To find: The position of particle at t=10. Given: The values are a(t)=18t+6, v(0)=15 and s(0)=15.…

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A: Using pythagoras theorem;Right angle triangle ABC, x2 + y2 =252      ....(1)

Q: A particle is moving with acceleration a(t)=12t+10. Its position at time t=0 is s(0)=8 and its…

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Q: A particle is moving with velocity v(t) = t2-9t + 18 with dista seconds inclusive. The position at…

A: To find the time interval when partical moving right .

Q: e3x d 6. (10) Calculate dx cot(t)dt. 2

A: Solve by using substitution and first solve the integral and then go for differentiation. Do step by…

Q: dy dt y = (t tant) ¹ Find 11

A: y= (t tant)11 y= t11 tan11tUsing formula ( d(uv) = uv'+vu' )diff w.r.t "t"dydt=t11.11tan10(t) sec2t…

Q: A particle is moving with acceleration a(t) = 6t + 4. its position at time t = 0 is s(0) = 14 and…

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Q: -, A particle starts at (5, 0) when t = 0 and moves along the x-axis in such a way that at time t >…

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Q: An automobile of mass M=5400 kg is moving at a speed of 30 m/s The engine is disengaged suddenly at…

A: As per the question we have to calculate the following integral : Integral of 5400v/(8.276v2 + 2000)…

Q: A particle is moving with acceleration a(t) = 30t + 10. its position at time t = 0 is s(0) = 7 and…

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Q: A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall…

A: calculate the cat fall ?

Q: = 10t – 10, where A particle moves along a line with velocity function v(t) v is measured in m/s.…

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Q: 69. Find the value of dr/dt at t= 0 if r= (02 + 7)3 and 0?t + 0 = 1.

A: Given: r=(θ2+7)13θ2t+θ=1drdt|t=0=?

Q: along the x-axis so that at time t 2 0, the acceleration of the particle is a(t) = 15Vr. ticle is 10…

A: In this question we will use basic concepts of calculus i.e concept of integration. We will use the…

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: d?s = 8 e 2t, initial velocity v(0) = 10, and initial position s(0) = 5. Find the position of a body…

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Q: A particle is moving with acceleration a(t) = 6t + 10. its position at time t = 0 is s(0) = 17 and…

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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: ds The position of a particle at time t is given by s. Find the velocity dt s4-7st+2t-3t= 0 ds dt

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Q: Solve the initial value problem for x as a function of t.. dx (? - 15t + 56). = 1 for (t> 8), x(9) =…

A: Given that      (t2-15t+56)(dx/dt) = 1 for (t>8), x(9)=0 Here we have to find the initial value…

Q: dV = 0.6t · cos(0.08t² – 1) , where V(t) is in dt 10) The rate of change in the volume of a tank is…

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Q: L4 + Ri = E,where L, R,and E are constants when t = 0,i = 0 dt

A: As we know that the solution for the linear differential equation dydx+Py=Q  is: yI.F.=∫QI.F.dx+C…

Q: At which times is the particle instantaneously motionless

A: Concept: The velocity is figured out by dividing the distance by the time taken to travel that same…

Q: ds The velocity of a particle moving back and forth on a line is v = = 6 sin(2t) m/sec for dt all t.…

A: Given:   To find:

Q: (d) The speed of an object ds / dt in (m/s) is given as: ds = 8t – 2 dt Given that it its position…

A: As you post multiple question according to guidelines I only solve the first question. please post…

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: The position of a particle at time t is s(t) = t3 + 4t over the time interval [2, 6] and estimate…

A: Obtain the average velocity of the given particle over the given interval as follows.

Q: A particle moves on the x axis with acceleration a(t)=6t-10 m/sec2 for t seconds over [0,10] with…

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Q: A particle is moving with acceleration a(t)=6t+12. its position at time t=0 is s(0)=14 and its…

A: a(t) = 6t + 12 at t = 0 : s(0) = 14 v(0) = 5 What is its position at time t=13?

Q: The volume V of a sphere of radius r changes over time t. a. Find an equation relating dV>dt to…

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Q: dN = 47(- N MV² -)dv 2RT M -)3/2v² exp(- 2 TRT F(V)dV : where dN, the number of particles having a…

A: Given: FVdV=4πM2πRT32V2e(MV22RT)dV Obtain: <V2>=∫0∞V2fVdV Compute the integral with…

Q: d*s ds Solve dt? +13s 0, where s is the displacement of an object at time t dt ds given that s = -1,…

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Q: A body is dropped (initial velocity being 0) from a distance ro from the earth's center. Ignoring…

A: The acceleration is given by . We can rewrite  using the chain rule as . Replace  in . Integrate…

Q: MV² dN F(V)dV = M 47(- 2 TRT -3/2 v? exp(- -)dv N 2RT Where dN, the number of particles having a…

A: Given: FVdV=dNN=4πM2πRT32V2e(MV22RT)dV Compute: V2=∫0∞V2FVdV…

Q: 29. A diesel car gradually speeds up so that for the first 10 s its acceleration is given by dv du…

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Q: 03. The acceleration of a particle moving along the r-axis is given by a(t) = (t – 8)sin t for 0SIS…

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Q: What is the rate equation for Newton's Law of Cooling? T is the temperature of the body and Tm is…

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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 particle is moving with velocity v(t) = t2-9t + 18 with distance, s measured in meters, left or…

A: The objective is to find instantaneous velocity and speed at time t=5sec.