- The position of an object moving on a line is given by s(t) = 6t2 – t°, t > 0,

Q: dy Find dæ Given that y = 3u² – 7u + 5 and u = 6a² + 4x – 1. 1. 2. Find an equation of the tangent…

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Q: ind an equation of the tangent to the curve parameter. 18. z = t, y = t² – 1; t= -4

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: Consider the curve in the xy-plane represented by the two equations below. The slope of the line…

A: Given: x=et……1y=te-t……2 where t≥0   To find: Slope of line tangent at x=3

Q: If the position curve is S(T) 27-157 +24T, (T: second) 1- Find acceleration and jerk at T=3 sec 2.…

A: The given position curve is ST=2T3-15T2+24T.

Q: Find an equation of the line tangent to the curve at the point corresponding to the given value of…

A: Given curve is Firstly, we will find value of x and y at t=3pi/4

Q: d'y Calculate the second derivative dr? for the plane curve defined by the equations #(t) = t and…

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Q: The velocity function (in meters per second) for a particle moving along a line is given by v(t) =…

A: Given, v(t)=t3-2t2   Interval [a,b]=[-2,3]

Q: a) What is the particle's position at time 2? b) What is the particle’s displacement from t= 1 to…

A: (a) The function representing the position is  X(t)=t3-15t2+48t. To find the position of the…

Q: 2. A particle is moving along a horizontal line such that its velocity is given by v(t) = 3t2 –…

A: Topic:- application of derivatives and integration

Q: Find the position and velocity of an object moving along a straight line with the acceleration a(t)…

A: Given

Q: A particle is moving along the x-axis according to s(t) = 1+ sin(t) where t is in seconds, t ≥ 0,…

A: Introduction: In calculus, a function's derivative measures how sensitively its output value changes…

Q: When d is in feet, t in second , find the velocity at t= 2 of the motion s = t^2 +3t

A: s=t2+3tVelocity of the particle isdsdt=2t+3On putting the value oft=2

Q: Suppose the velocity of a particle at time t is given by 3/19 (t+1) + VI+1 7(1) tan(t) %3D 1+ t2

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Q: The time of oscillation, 1, of a pen- dulum is given by t 27 1. wherel is the length %3D of the…

A: Write this equation in standard form then diffrenciate.

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 of a particle at time t is given by a(t) = 4e2t¸ If the initial velocity was 5, and…

A: We will use integration to first find the velocity and then integrate velocity function to find…

Q: Find the interval on which the curve dt 3 +t + 212 y = is concave upward.

A: Given: y=∫1x13+t+2t2dt

Q: Two particles have positions at a time t given by the equations x1=t3-t and x2=6t2-t3 find the…

A: If x(t) represents position at time t then velocity = v(t) = dx/dt and acceleration = a(t) = dv/dt =…

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: Find the displacement of an object over the time interval, [T/4, T/2], given the velocity function,…

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Q: A particle moves on the x-axis with velocity given by v(t) = 3t4 − 11t2 + 9t − 2 for −3 ≤ t ≤ 3 .…

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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: 7. a. Find the points on the curve x = 3(t2 – 3), y = t³ – 3t where the tangent is horizontal or…

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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: 9. The velocity, in kilometers per hour, of a car as it beings to slow down is given by the equation…

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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 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 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: - The position of an object moving on a line is given by s(t) = 6t2 – t°, t> 0,

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Q: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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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: The velocity function (in meters per second) is given by v(t) = t2 - 2t - 3, for a particle moving…

A: We will use formula for the Displacement and distance in terms of Velocity function

Q: Let s(t) = V9 t. Find the equation of the tangent line to s(t) when t = 0. %3D y =

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Q: The velocity of an object in meters per second is given by v(t) 25-, 0sts5. Find: %3D a) The…

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Q: (2.;v3). 1 Find the equation of the tangent line to x? +y²: = 1 at Use exact values in y = mx + b…

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Q: Suppose velocity of a car starting from rest is modelled by equation V(t)= In(4t^3 + 1) m/s What…

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Q: If the position of a particle of mass m at time t seconds is given by 7= (r +1)i- 2j + ik, which of…

A: The position vector of the particle is given by, r→=t2+1i−2tj+t2k

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: Q-1-At time t, the position of a body moving along the s - axis is t4 9. S = - 2t3 2t3 +t2 + 5t -- 4…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

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 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: If position is given by p(t)=-t^2+5t what is the velocity v(t) at t=2?

A: The position is p(t)=-t2+5t

Q: Given a particle is moving in a curve r(t) = cos 2t i + sin 2t j + 8t k. Find the tangential…

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Q: The velocity (in feet per second)of a partice moving along a line is v(t) = t – 10t² +29t – 20 -…

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Q: A particle moving on a line is at position x(t)=t3−9t2+24t−5 at time t where t is in seconds. At…

A: The given function for position of an object is where t is the time in seconds. Now, to find points…

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: 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: A particle moves in a straight line with velocity v(t)=t2 How far does the particle move between…

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