   Chapter 13.4, Problem 20E

Chapter
Section
Textbook Problem

# What force is required so that a particle of mass m has the position function r(t) = t3i + t2j + t3k?

To determine

To find: The required force so that a particle of mass m has the position function r(t)=t3i+t2j+t3k.

Explanation

Given:

r(t)=t3i+t2j+t3k

Formula used:

Write the expression to find the acceleration,

a(t)=r(t)

a(t)=d2dt2[r(t)] (1)

Write the expression for the second law of motion,

F(t)=ma(t) (2)

Here,

F(t) is the force,

m is the mass, and

a(t) is the acceleration.

Substitute t3i+t2j+t3k for r(t) in equation (1),

a(t)=d2dt2(t3i+t2j+t3k)=ddt[ddt(t3i+t2j+t3k)]=ddt[ddt(t3)i+ddt(t2)j+ddt(t3)k]=d

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