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Chapter 11: Q. 30 (page 872)

Find the velocity and acceleration vectors for the position vectors given in Exercises 30鈥�34

30.r(t)=鉄�t,t2,t3鉄�

Short Answer

Expert verified

The velocity and acceleration vectors are;

v(t)=鉄�1,2t,3t2鉄�a(t)=鉄�0,2,6t鉄�

Step by step solution

01

Step 1. Given data

The given position vector isr(t)=鉄�t,t2,t3鉄�

We have to find the velocity and acceleration vectors.

02

Step 2. Velocity vector

The velocity vector v(t) is given by

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

Therefore,

v(t)=ddtr(t)=ddt鉄�t,t2,t3鉄�=鉄�ddt(t),ddt(t2),ddt(t3)鉄�=鉄�1,2t,3t2鉄�

Hence the velocity vectorv(t)=鉄�1,2t,3t2鉄�

03

Step 3. Acceleration vector

The acceleration vector a(t) is given by,

a(t)=ddtv(t)

Therefore,

a(t)=ddtv(t)=ddt鉄�1,2t,3t2鉄�=鉄�ddt(1),ddt(2t),ddt(3t2)鉄�=鉄�0,2,6t鉄�

Hence, the acceleration vector isa(t)=鉄�0,2,6t鉄�

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