The position of a particle is given by s(t) = t³ – 20.5t² – 2t, t > 0. When does the particle reach a velocity of – - 77.68 m/s?

Q: The position of a moving particle is given by s(t) = t2 – 7t + 4 on the interval 0 <t< 4, where 's'…

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Q: The temperature at point (x, y) is given by T(x, y) = 100 – 3x² – y³. Find the direction from point…

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

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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: a ball is thrown straight upwards from a tower (40 feet high) so that its position, s in feet, at…

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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: The position of a moving particle is given by s(t) = 2t2 – 18t on 2 <t< 9 where 's' is in meters and…

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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: 2. A body moves along the straight path. If the given initial velocity is 2t2 – 4t + 5, what is the…

A: Given initial velocity is     vt = 2t2-4t+5As we know that velocity is rate of change of…

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: Solve the problem. A body of mass m is moving in a straight line with an initial velocity of 2 m/s…

A: Given:-   acceleration⇒6t2-2t+4initial  velocity  of 2m/sec  from origin at  t=0,a=acceleration;…

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: A particle moving along a line has the position s(t) = t* – 1812 at time t seconds. What is the…

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Q: s(t)%3D512 +t3 :-

A: Given information: st=5t2+t3 Find the velocity at -2.

Q: dv dt    = −kv2 An object moving through the water has an initial velocity of 40 m/s. Two seconds…

A: As the given differential equation is: dvdt=-kv2 Given conditions are:  t=0 , v=40 mst=2s, v=30 ms…

Q: The position of the particle at time t is given by s(t) = t² – 6t + 8. The particle is moving from…

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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) = 6t – 6t for time t > 0. If the…

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Q: The position of the particle at time t is given by s(t) = t² – 18t + 80. %3D The particle is moving…

A: The particle will move from left to right if the velocity is positive

Q: The position of a moving particle is given by s(t) = t2 – 7t + 5 on the interval 0 <t< 5, %3D -…

A: First I have find the Instantaneous velocity and then Average velocity then making them equal and…

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 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: The position of the particle at time t is given by s(t) = t2 – 16t + 63. The particle is moving from…

A: t=10.0 seconds

Q: The position of the particle at time t is given by s(t) = t² – 8t + 15. %3D The particle is moving…

A: Concept used particle will move fromleft to right when velocitydvdtbecome positive.dsdt&gt;0

Q: A population of bacteria is growing according to the equation P(t)=1350e^0.11t Estimate when the…

A: Substitute P(t)=2418 into the equation Pt=1350e0.11t and solve for t:…

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: At time t sec, the positions of two particles on a coordinate line are s1 = 3t3 - 12t2 + 18t + 5 m…

A: To find velocity we have to differentiate the distance s with respect to t.

Q: The position of a moving particle is given by s(t) = t2 – 2t + 6 on the interval 0 <t < 6, - where…

A: We will solve the following.

Q: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s^2 is…

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Q: at time t20, the velocity of a body moving along the s-axis is v=t - 7t+ 6. When is the body's…

A: Explanation and solutions is given below....

Q: A particle moves along the x-axis so that at time t ≥ 0, its position is given by x(t) = 2t3 - 3t2.…

A: V(t) = d[x(t)]/dt Put, v(t) &gt; 0.

Q: nen does the particle reach a velocity of 137 m/s if its position function is given by:…

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Q: s = -t² + 6t –1 and 0<t <1 then the velocity at t = 1 is

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Q: Find the displacement of a particle moving in a straight line with velocity v(t) = 4t - 3 mis over…

A: Given velocity of particle is vt=4t-3. To find the dispalcement of particle over time interval 2,5.…

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 along a straight horizontal line so that its position at any time is given by s(t)…

A: Let's find.

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

A: The given data isVt=10t4-tt+1t-7m/s.To find:The distance travelled by particle over interval t∈0,6.

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

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Q: Determine the velocity of the particle at t = 7.

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Q: (a) What is the particle's position at t = 0? (b) What is the particle's position at t = 3? (c) What…

A: Since you have asked multiple part question, we will solve the first 3 part of the question for you…

Q: A particle moves along the x-axis with velocity given by v(t) = 6t² + 1 for time t > 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: 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: At time t seconds, the center of a bobbing cork is 2sin(2t) centimeters above or below water level.…

A: ft=2sin2t Now velocity is the derivative of position with respect to time. So differentiating…