Question

For the equation below, r(t) is the position vector of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0. r(t) = (3 \ln (t^2 + 1))\mathbf{i} + (\tan^{-1} t)\mathbf{j} + 8\sqrt{t^2 + 1}\mathbf{k} The angle between the velocity and acceleration vectors is (Type an exact answer, using \pi as needed.)

          For the equation below, r(t) is the position vector of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0.
r(t) = (3 \ln (t^2 + 1))\mathbf{i} + (\tan^{-1} t)\mathbf{j} + 8\sqrt{t^2 + 1}\mathbf{k}
The angle between the velocity and acceleration vectors is 
(Type an exact answer, using \pi as needed.)

For the equation below, r(t) is the position vector of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0.
r(t) = (3 ln(t^2 + 1))𝐢 + (tan^-1 t)𝐣 + 8√(t^2 + 1)𝐤
The angle between the velocity and acceleration vectors is
(Type an exact answer, using πas needed.)

Added by Todd S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Adi S

09/13/2022

Step 1

Since ni is a constant vector, its derivative with respect to time is zero: ni' = 0 Therefore, the velocity vector simplifies to: v(t) = a'(t)ni + a(t)ni Show more…

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For the equation below, r(t) is the position vector of a particle in space at time t. Find the angle between the velocity and acceleration vectors at time t=0. r(t) = 3i^2 + 11j + a(t)ni + 8(1 + k) The angle between the velocity and acceleration vectors is (Type an exact answer, using âˆš as needed.)