   Chapter 16.2, Problem 43E

Chapter
Section
Textbook Problem

The position of an object with mass m at time t is r(t) = at2 i + bt3j, 0 ⩽ t ⩽ 1.(a) What is the force acting on the object at time t?(b) What is the work done by the force during the time interval 0 ⩽ t ⩽ 1?

(a)

To determine

To find: The force acting on the object at time t .

Explanation

Given data:

The position of an object with mass m at time t is r(t)=at2i+bt3j,0t1 .

Formula used:

Write the expression to find the force vector.

F(t)=ma(t) (1)

Here,

m is the mass of the object and

a(t) is the acceleration vector of the object.

Write the expression to find acceleration vector of the object.

a(t)=ddt[v(t)] (2)

Here,

v(t) is the velocity vector of the object.

Write the expression to find velocity vector of the object.

v(t)=ddt[r(t)] (3)

Here,

r(t) is the position vector of the object.

Calculation of v(t) :

Substitute at2i+bt3j for r(t) in equation (3),

v(t)=ddt[at2i+bt3j]=ddt(at2)i+ddt(bt3)j

(b)

To determine

To find: The work done by the force on the object during the time interval 0t1 .

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