Let r(t) = 2t ,4t2 ,2t be a position function for some object. (a) (2 pts)...

Let r(t) = 2t ,4t2 ,2t be a position function for some object.

(a) (2 pts) Find the position of the object at t = 1. (b) (6 pts) Find the velocity of the object at t = 1.

(e) (15 pts) Find the curvature K of the graph C determined by r(t) when t = 1.

Solutions

Expert Solution

milcah answered 1 year ago

Next > < Previous

Related Solutions

Let L be the line parametrically by~r(t) = [1 + 2t,4 +t,2 + 3t] and M...

Let L be the line parametrically by~r(t) = [1 + 2t,4 +t,2 + 3t] and M be the line through the points P= (−5,2,−3) and Q=(1,2,−6). a) The lines L and M intersect; find the point of intersection. b) How many planes contain both lines? c) Give a parametric equation for a plane Π that contains both lines

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t)...

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t) from t = 0 to t = 5. SET UP integral but DO NOT evaluate • What is the curvature κ(t)?

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

Let r : R->R3 be a path with constant speed, satisfying r"(t) = (4 sin(2t))i +...

Let r : R->R3 be a path with constant speed, satisfying r"(t) = (4 sin(2t))i + (-4 cos t)j + (4 cos(2t))k for all t belongs to R: Find the curvature w.r.t. t of r. (Hint: cos(2t), sin(2t), and cos(t) are linearly independent. i.e. if c1cos(2t) + c2sin(2t)+ c3cos(t) = 0 for all t belongs to R, then c1 = c2 = c3 = 0.)

Find the curvature of the parametrized curve ~r(t) =< 2t 2 , 4 + t, −t...

Find the curvature of the parametrized curve ~r(t) =< 2t 2 , 4 + t, −t 2 >.

Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the...

Given the vector function r(t)=〈√t , 1/(t-1) ,e^2t 〉 a) Find: ∫ r(t)dt b) Calculate the definite integral of r(t) for 2 ≤ t ≤ 3 can you please provide a Matlab code?

The position of a particle is r={(3t3−2t)i−(4t1/2+t)j+(3t2−2)k}m, where t is in seconds. Part A Determine the...

The position of a particle is r={(3t3−2t)i−(4t1/2+t)j+(3t2−2)k}m, where t is in seconds. Part A Determine the magnitude of the particle's velocity when t = 0.5 s . Express your answer with the appropriate units. v=? Part B Determine the magnitude of the particle's acceleration when t = 0.5 s . Express your answer with the appropriate units. a=?

Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of...

Let T: R^2 -> R^2 be an orthogonal transformation and let A is an element of R^(2x2) be the standard matrix of T. In a) and b) below, by rotation we mean "rotation of R^2 by some angle and the origin". By reflection, we mean "reflection of R^2 over some line through the origin". a) Show that T is either a rotation or a reflection. b) Show that every rotation is a composition of 2 reflections, and thus that T...

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the...

Consider the vector function given below. r(t) = 2t, 3 cos(t), 3 sin(t) (a) Find the unit tangent and unit normal vectors T(t) and N(t). T(t) = N(t) = (b) Use this formula to find the curvature. κ(t) =

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function...

The function sequals=?f(t) gives the position of an object moving along the? s-axis as a function of time t. Graph f together with the velocity function ?v(t)equals=StartFraction ds Over dt EndFractiondsdtequals=f prime left parenthesis t right parenthesisf?(t) and the acceleration function ?a(t)equals=StartFraction d squared s Over dt squared EndFractiond2sdt2equals=f prime prime left parenthesis t right parenthesisf??(t)?, then complete parts? (a) through? (f). sequals=112112tminus?16 t squared16t2?, 0less than or equals?tless than or equals?77 ?(a heavy object fired straight up from? Earth's...

Subjects