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Chapter 11: Q. 9 (page 901)

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

r(t)=鉄�t,2t-3,3t+5鉄�

Short Answer

Expert verified

Ans:v(t)=鉄�1,2,3鉄�anda(t)=鉄�0,0,0鉄�

Step by step solution

01

Step 1. Given information: 

r(t)=鉄�t,2t-3,3t+5鉄�

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�t,2t-3,3t+5鉄�

localid="1649657595879" v(t)=ddt(r(t))=ddt鉄�t,2t-3,3t+5鉄�=ddt(t),ddt(2t-3),ddt(3t+5)=鉄�1,2,3鉄�a(t)=ddt(v(t))=ddt鉄�1,2,3鉄�=ddt(1),ddt(2),ddt(3)=鉄�0,0,0鉄�

thus

v(t)=鉄�1,2,3鉄�anda(t)=鉄�0,0,0鉄�

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Most popular questions from this chapter

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