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Chapter 11: Q. 12 (page 901)

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

r(t)=et,t,e-t

Short Answer

Expert verified

r(t)=et,t,e-tAns:v(t)=et,1,-e-tanda(t)=et,0,e-t

Step by step solution

01

Step 1. Given information: 

r(t)=et,t,e-t

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)=et,t,e-t

v(t)=ddtr(t)=ddtet,t,e-t=ddtet,ddt(t),ddte-t=et,1,-e-ta(t)=ddt(v(t))=ddtet,1,-e-t=ddtet,ddt(1),ddt-e-t=et,0,+e-t

thus

v(t)=et,1,-e-tanda(t)=et,0,e-t

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