The displacement function of the motion of a particle is given as t3 s(t) – 2t² + 4t – 6 - 3 Assuming the reference of s(t) is the origin. Find the following: a. The velocity function v(t); b. The time interval during which the object is moving to the left;

Q: m Find the equation of the tang ent to the curve ym =1 at the point (x1.y1). m

A: Topic:- application of derivatives

Q: where is in seconds, and v is a. Is the particle speeding up or slowing down at t = 5? b. If the…

A: Given that a particle is moving along a horizontal line such that its velocity is given by…

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: 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: The position function of a particle is giyen by s(t) = (t – 1)²(t – 3) , where t is measured is…

A:

Q: A particle moves along the x-axis with acceleration at any given time t as a(t) = 3t+4t+6,jf the…

A:

Q: For the position function, s(t)=-16t2+103t​, complete the following table with the appropriate…

A: Consider the position function, s(t) = 16t2+103t.

Q: The movement of a particle from time t=0 to t=9 is given by the equation s(t)=−5t2−5t−10. What is…

A:

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 a horizontal line such that its velocity is given by v(t) = 3ť² – 24t+36,…

A: Let's find.

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…

A:

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

A: to find the slope of the tangent we will need dy/dx. For that we find dx/dt and dy/dt first

Q: A. If r = r(t) represents the position function at time t of a certain particle, then what do you…

A: first derivative of position gives- velocity

Q: Suppose an object moves along the x-axis so that its position at time t is x = −t +t3/6 (a) Find…

A: Note: There are many subparts in the questions so I will answer the first three questions and other…

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

A: Solve

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

A:

Q: The position function of an object is given by s(t) = -t + 2t. For t > 0 and s(t) = 0m, the velocity…

A:

Q: given the position function for an object in motion  is s(t)=-4t3+4t2-1 then the accelaration at t=1…

A: Differentiate the position function with respect to time t.

Q: (2) A particle moves along the 1-aris such that the velocity is given by v(t) = 20e' +t for t > 0.…

A: Here, the velocity vector is: v(t)=20et+t7

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>0

Q: For the position function s(t) = - 16t + 113t, complete the following table with the appropriate…

A: We need to find average velocity values and fill the table.

Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

A:

Q: A ball is dropped from a 200 foot cliff. If gravity is 32 ft/sec2, find the position function of the…

A: Given :- Initial height of ball (S0)= 200 feet Accelaration due to gravity(g) = 32 feet/sec2…

Q: The position function of a particle is given by s(t) = 3t2 – t3, t > 0. (a) When does the particle…

A: The given position function is:  s(t)=3t2-t3So, the velocity function…

Q: For the position function s(t) = - 16t + 114t, complete the following table with the appropriate…

A:

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

A: zt=7t-7t2

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

A:

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

A:

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

A:

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

A:

Q: The x- coordinate of the point on the graph of y = Vx-1 at which the tangent line is perpendicular…

A: slope of tangent of the curve y=x-1 is dydx=12x-1 slope at (x1, y1)dydx=12x1-1=m1if (x1, y1) is the…

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

A:

Q: (b) f(x)= e²**1 at P (In 2, 4e) 2.x+1 3De

A:

Q: The position function of a particle is given below. s(t) = t3 + 1.5t2 - 55t, tz 0 %3D When does the…

A:

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

A: Equation of tangent line at (x0,y0) (y-y0) = m(x-x0)

Q: For the position function s(t) = - 16t + 110t, complete the following table with the appropriate…

A: Consider the position function

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

A:

Q: The position function of a particle is given by = t3 – 10.5t2 – 2t, t > 0 When does the particle…

A:

Q: Suppose an object is moving along a line, and its acceleration at time t is given by a(t) = 3t – 6,…

A:

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

A: Then we plug t=-1

Q: The position function of a particle is given by s(t)=t^3−4t^2−8t, t≥0 where s is measured in meters…

A: To find the velocity function from the position function, we have to differentiate position function…

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: nd s(t), where s(t) represents the position function, v(t) represents the velocity function, and…

A:

Q: x = VE, y = t? – 2t; t = 16

A:

Q: Find the linear approximation to the equation f(x, y) = 4xy – 6xy? at the point (2,1,-4), and use it…

A:

Q: The acceleration of a particle traveling along the x-axis is given by a(t) = t2 - 2t. What is the…

A: Given: Acceleration function is a(t)=t2-2t. Acceleration function is also written as: dvdt=t2-2t.…

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

A: x=et , y=t-lnt2,  t=1 Differentiating with respect to t, we get dxdt=detdt  &…

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

A:

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

A: Using formula of equation of tangent line.