Find the velocity and the acceleration at time t = 4 s for the position function s(t) = V +5. v(4) =

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: A particle moves on a vertical line so that its coordinate at time t is y = t – 12t + 3, t 2 0,…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

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: 6. Find the position function of a particle moving along a coordinate line whose velocity at time t…

A: The velocity of the particle is given as a function of time by, v=6t2-4t+4 The velocity of a…

Q: The position of a particle moving along the x-axis is given by 4 37 x(t) = (t – 1)* +(t – 1)³ – 12(t…

A: Hello. Since your question has multiple sub-parts, we will solve first three sub-parts for you. If…

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: A particle moves along a straight line and has acceleration given by s" = 5t. Its initial velocityis…

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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: A particle moving along the x-axis has position function p(t)=−t^3+t^2+2t+1. Find the acceleration…

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Q: The position of a particle at time t (s) is s(t) = t2 + 1 m. Compute its average velocity over [2,…

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Q: a particle moves according to the function s(t)= t^2 - 2t +5,  what is the instantaneous velocity of…

A: A particle moves according to the function s(t)=t2-2t+5

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: b) Use the velocity function v(t) = 2e" to compute the distance traveled by an object over the time…

A: The detailed solution is given below  Thank you

Q: The acceleration function of a particle moving along a line is given by: a ( t ) = 2 t + 3 in m / s…

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Q: Find velocity (f'(x)) and acceleration (f''(x)) at time or t=0 with equation s(t)=2((e^t)-(e^-t))

A: We have to find velocity and acceleration

Q: The value of the instantaneous velocity at t = 1 is

A: Consider the position function To calculate the instantaneous velocity

Q: If the position of a moving particle at any time 't' is defined by s(t) 3t-9t,0<t<6. The…

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

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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: A particle is moving with acceleration a(t) 24t+12. its position at time t = 0 is 8(0) = 13 and its…

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Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: For the given velocity  v(t) = 10t +12 for t&gt;=0 if the position is x =2  at time t = 0  Position…

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 moves along the x-axis with its position measured relative to the origin and has an…

A: To find: The velocity and position after t=1 second: Given: The acceleration of the body is at=6t+4…

Q: A particle moves along the x-axis so that at time t\ge 0t≥0 its position is given by…

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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 moves on a vertical line so that its coordinate at time t is y = t³ – 12t + 3,t > 0,…

A: Speeding up and slowing down is depend on the acceleration of particles so first find the…

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 moves along a straight line and has acceleration given by s"(t) = 5t +3- Its initial…

A: Given,  s''(t)=5t+3, s'(0)=-4, s(0)=7

Q: Suppose the function p(t)=(t^2 - 2)e^2t represents the position of a particle at time t. Determine…

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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 position is given by x(t) = -t3 +11t?…

A: For the given position vector  x(t) = -t3+11t2-24t Velocity at t = 7 is calculated as shown below

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: 1. The position of a particle at time t is given by s(t) = t³ – t2. Using a table, estimate the…

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Q: A particle moves along the x-axis with velocity given by v(t) = 10t + 12 for time t> 0. If the…

A: Given: The velocity of the particle along x-axis is vt=10t+12 The particle is at the position x=2 at…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t2 – 18 for time t > 0. If the…

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Q: A particle moves in a straight line and has acceleration given by a(t)=12t+2. Its position at time…

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Q: The position of a particle at time t is s(t) = 4t^3. Compute the average velocity over the time…

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Q: The position of a body moving along s-axis at any time 't' is given by s(t) = 16t3 – 12t, - then the…

A: We will find out the required value.

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² – 10t for time t> 0. If the…

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Q: A particle is moving in a straight line with the velocity v(t) =1-t,0<t< 3. Compute the distance…

A: We have V=1-t⇒dxdt=1-t∫0△xdx=∫(1-t)dt

Q: Determine the position function if the acceleration function is a(t) = 6sin t+5, the initial…

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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: The position of a particle at time t is s(t) = 4t^3. compute the average velocity over the time…

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Q: At time t ≥ 0, the velocity of a body movingalong the horizontal s-axis is v = t2 - 4t + 3. When is…

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Q: The position of a body moving along s-axis at any time 't is given by s(t) = 16t - 12t, then the…

A: The position of a body s(t)=16t3-12t

Q: A particle moves along the x-axis so that at time t 0 its position is given by a(t) = -t + 4ť² – 4t.…

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