The velocity function (in meters per second) for a particle moving along a line is given by v(t) = t³ – 2t². Find the displacement and the distance travelled by the particle during the time interval [-2,3].

Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 3t…

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Q: Find the derivative dydx for the function x=1t+t, y=1t2 at the point t=12.

A: Here given

Q: Suppose that a particle moves along a straight line with velocity defined by v(t) = t2− 3t − 18,…

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Q: Find the linear approximation of the function f(x) = /1 – x at a = 0 and use it to approximate the…

A: Given,

Q: Consider the function f(x, y) = y³ – 2y – x². Find the direc- tion of greatest increase at the point…

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Q: The velocity function (in meters per second) is given for a particle moving along a line. v(t) = 5t…

A: Given:The velocity function of the particle is v(t) = 5t-8.

Q: Calculate the differential of the function y=x5−7x3+5x at the point x=2 when dx=0,2.

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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: A particle starts from rest and moves in a straight line such that the acceleration, a, in m/s2 ? =…

A: To find: The instantaneous velocity at t=2. Given: The acceleration of particle is a=12t2-24t+8.…

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

A: Solve

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 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: 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: The velocity function is v(t)=t2 +6t+8 for a particle moving along a line. Find the displacement…

A: We have to find out the displacement

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 derivative of the function at P0 in thedirection of v. ƒ(x, y) = 2xy - 3y2, P0(5, 5), v =…

A: The given function is ƒ(x, y) = 2xy - 3y2. Note that fx=2y    and  fy=2x-6y. at P0=5,5,  fx=10   and…

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: c) Use the velocity function v(t)= 2e2m/s to compute the distance traveled by an object over the…

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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: 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: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: Apply the 1t derivative property to : 1) f(t) = e-2tsin5t 2) f(t) = = cost sint 3) f(t) = e²tsin2t…

A: Solution

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>=0 if the position is x =2  at time t = 0  Position…

Q: The velocity of a ball projected upward from ground level is given by v(t) = −32t + 48, where t is…

A: We know that, the rate of change of distance with respect to time is called velocity. That if s…

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: (b) If a rock is thrown upwared on the planet mars with a velocity of 12ms, its height in meters t…

A: The height of the rock is given by: y(t)=12t-1.92t2 To find the average velocity over the interval…

Q: Find the differential of the function. z = 7t − 7/t2

A: zt=7t-7t2

Q: dt F(x) = | 6+ 8t Find the interval on which the curve is concave downward.

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Q: Find the displacement of an object on the interval 0 ≤ t ≤ 6 if its velocity is v (t) = 4t -√√t

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Q: The distance of a body travels as a function of time and is defined by x(t) = 18t + 9t^2. What is…

A: Given that: Distance travelled by the body is given by:             x(t)=18t+9t2

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: 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: The position function of a particle is given by s(t) = 3t2 - t°, t 2 0. (a) When does the particle…

A: This question is based on derivative application.

Q: Given the acceleration of an object and its initial velocity, how doyou find the velocity of the…

A: We know that the rate of change of velocity of a moving particle is known as its acceleration. Let…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

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

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Q: dw B) Use the chain rule to find the derivative dt of w = x2 + y2 with x cost, y = sint.

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Q: Q11) For the z= (2x+3y)10,which is correct ?partial derivative

A: Given,  z = (2x + 3y)10 To find the partial derivatives.

Q: Determine the length of the curve TC f(x) = In[sec(x)],0 < x < 4

A: The given curve is- f(x)=lnsec(x)Interval 0≤x≤π4We need to determine the length of the given…

Q: Find the directiona derivative of f (x, y) = In(e* – 4y at the point (0, 0) %3D - in the direction…

A: We have to solve

Q: Find the average velocity of an object for the interval 1<t< 3, if its position is given by s = = t²…

A: Differentiate the function to find the velocity function. dsdt=2t+5

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: Consider an object moving along a line with velocity v(t) = 6t2 – 12t with t measured in seconds and…

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Q: 3. If f (t) = -t² + 5t + 3, describes the distance that a ball has traveled in meters, what is the…

A: Given : The function ,ft=-t2+5t+3 describes  the distance travelled by the ball in meters. To find:…

Q: A particle moving in a straight line is at a distance of s(t) = 1.lt³ + 13t feet from its starting…

A: The solution is given in next step

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…