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Chapter 11: Q. 11 (page 901)

Velocity and acceleration vectors: Find the velocity and acceleration vectors for the given vector functions.

r(t)=(cos2t,sin3t)

Short Answer

Expert verified

Ans:v(t)=鉄�-2sin2t,3cos3t鉄�anda(t)=鉄�-4cos2t,-9sin3t鉄�

Step by step solution

01

Step 1. Given information: 

r(t)=(cos2t,sin3t)

02

Step 2. Denoting the velocity and acceleration of the vector:

The velocity vector, v(t) is given by

v(t)=ddtr(t)=ddtx(t),ddty(t),ddtz(t).

That is, we take the derivative of each component function of r(t).

The acceleration vector, a(t) is given by

a(t)=ddtv(t).

That is, a(t)is obtained by taking the derivative of each component function of v(t).

03

Step 3. Finding the velocity and acceleration of the vector: 

Consider r(t)=鉄�cos2t,sin3t鉄�

v(t)=ddtr(t)=ddt鉄�cos2t,sin3t鉄�=ddt(cos2st,sin3t)=ddtcos2t,ddt(sin3t)=鉄�-2sin2t,3cos3t鉄�a(t)=ddt(v(t))=ddt鉄�-2sin2t,3cos3t鉄�=ddt(-2sin2t),ddt(3cos3t)=鉄�-4cos2t,-9sin3t鉄�

thus

v(t)=鉄�-2sin2t,3cos3t鉄�anda(t)=鉄�-4cos2t,-9sin3t鉄�

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Most popular questions from this chapter

Evaluate and simplify the indicated quantities in Exercises 35鈥�41.
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