he position x(t) of an object moving in 1-D on the a - aris in an inverse-square force held (such as an electromagnetic field) is given by Assume that the initial position of the object is known, i.e. = xo > 0. Show that the velocity of the body at time t is given by v(t) = 2k² (G-)-

Q: Another particle has a velocity function of v(t) = [' 2'-* dx. What is the acceleration of this…

A:

Q: An object is moving in the air (defying gravity) so that its height after t seconds is given by…

A: Answer :- A)Answer

Q: Find the derivative of the vector function r(t) = ln(19 - t²)i + √17+tj − 7e-¹t k - r' (t) = (¯¯

A:

Q: f(x)=x+5 glx)=x -1

A:

Q: Suppose you are given a vector-valued function modelling the velocity of a particle in space. At…

A:

Q: Find the equation of the tangent line to y = = at x = 1. y - V2 = - V7 (x - 1) A) E (x - 1) -- x y -…

A: The solution is given as

Q: suppose cX) is valued function on such that f?E R Faib] Does it fallows bounded real taib] that…

A: In the given question given that f(x) is a bounded real valued function on [a,b] then we have to…

Q: Find f. f ''(t) = 9/ squareroot t,    f(4) = 31,    f '(4) = 12

A:

Q: Let c(t) = (t^3 + 1, t^2 − 4t). Find:(a) An equation of the tangent line at t = 3

A: c(t)=t3+1 , t2-4t

Q: Sketch the curve r(t)=f°i+tj and indicate the orientation. Find r'(t) and sketch r(1) & r°(1).

A: First we will plot the given parameters.

Q: Find the direction field for the equation: y' = x + sin(y) + cos (x) at the point A = (0, pi3)

A: The direction field also known as slope field is used to graphically represent the solutions of…

Q: Find the derivative of the function T(z) = az + b cz + d' numbers such that ad – bc ‡ 0. When is…

A:

Q: Question 6 Prior to running the Boston Marathon, a runner's personal best pace for a race is 10…

A: Given that Prior to running the Boston Marathon, a runner’s personal best pace for a race is 10…

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: Consider a particle moving along a curve so that it is at position f(t) = (2t³, 2+²) at time t. Then…

A: Given, A particle is moving along a curve such that its position is at ft=2t3,2t2 at time t.

Q: Find the derivative of r(t)=(5-1³) î+2te¹¹ ĵ+sin 31 k and find the unit tangent vector at the point…

A:

Q: Compute the derivative: 4 te* dt d 3z2 L tet dz -1

A:

Q: Find the equation of the tangent plane to z= e" +x+x³ +1 the point (2, 0, 12).

A: Let a surface be represented by the function fx, y, z = c where c is a constant. Then the equation…

Q: By differentiation with respect to time, show that the equation x = xi + ut + 1/2 at² describes…

A: Given that, x=xi+ut+12at2. Where, xi is the initial position. u is the initial speed a is the…

Q: Consider the following problem from Science: A mitochondria with velocity vector r' (t) starts out…

A:

Q: Find the zeros of Q(x) = 5x - x² + 9 using the quadratic formula. Number of zeros: one

A: Given Quadratic formula is Q(x)=-x2+5x+9 Compare to ax2+bx+c=0 Here a=-1, b=5 and c=9.