   Chapter 13.4, Problem 14E

Chapter
Section
Textbook Problem

# Find the velocity, acceleration, and speed of a particle with the given position function.14. r(t) = ⟨t2, sin t − t cos t, cos t + t sin t⟩, t ≥ 0

To determine

To find: The velocity of a particle.

Explanation

Given:

r(t)=t2,sinttcost,cost+tsint.

Formula used:

Write the expression to find the velocity.

v(t)=r(t)

v(t)=ddt[r(t)] (1)

Substitute t2,sinttcost,cost+tsint for r(t) in equation (1),

v(t)=ddt(t2,sinttcost,cost+tsint)=ddt(t2),ddt(sinttcost),ddt(cost+t

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