Chapter 6, Problem 5RAT

Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving box slides across a post office floor and comes to a stop?

(a)F = ma

(b) $Ft=\Delta mv$

(c) $KE=1/2m{v}^2$

(d) $Fd=\Delta 1/2m{v}^2$

To determine

The correct option for the statement "Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving box slides across a post office floor and comes to a stop?"

Answer to Problem 5RAT

The correct option for the statement "Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving box slides across a post office floor and comes to a stop?" is option (d).

Explanation of Solution

The work-energy theorem states that the work done by an object is equal to the change in the kinetic energy of the object. The work done on the object is same as the product of force acting on the object and the displacement of the object. The change in the kinetic energy is equal to the difference of final kinetic energy and initial kinetic energy.

The given expression in the option (a) describes only the force on the object, so it does not describe the solution for the distance of fast-moving box.

The given expression in the option (b) describes the impulse-momentum equation, which is not enough for the solution of the movement of the fast-moving box.

The given expression in the option (c) describes the kinetic energy of the object, so it does not solve the problem for the distance of the fast-moving box.

The given expression in the option (d) describes the work-energy equation, which is enough to solve the problem of the distance of the fast-moving box.

Conclusion:

Therefore, the correct option for the statement "Which of the following equations is most useful for solving a problem that asks for the distance a fast-moving box slides across a post office floor and comes to a stop?" is option (d).