Chapter 14, Problem 106A

(a)

To determine

To Calculate: Final kinetic energy of the automobile.

Answer to Problem 106A

Kinetic energy is $8.8\times {10}^6$ J.

Explanation of Solution

Given:

Mass of the automobile, $m=1400$ kg.

Final speed of the automobile, $v=112$ m/s.

Formula used:

  $KE=\frac{1}{2}m{v}^2$

where,

KE: Kinetic energy

m: mass

v: speed

Calculation:

Substitute the values in above formula and solve:

  $KE=\frac{1}{2}(1400)\times {(112)}^2$ J

  $KE=8.8\times {10}^6$ J

Conclusion:

Hence, the final kinetic energy of the automobile is $8.8\times {10}^6$ J.

(b)

To determine

To Explain: Minimum amount of work done and the reason for no possibility to calculate the total amount of work done.

Answer to Problem 106A

Minimum amount of work done is $8.8\times {10}^6$ J.

Explanation of Solution

Introduction:

As work done is equal to the change in the kinetic energy, the minimum amount of work done shall equal to that of kinetic energy i.e. $8.8\times {10}^6$ J.

The engine had to do more work than that was consumed in work done against friction. Thus, it is not possible to calculate the total work done.

Conclusion:

Minimum amount of work done is $8.8\times {10}^6$ J.

(c)

To determine

To Calculate: The average acceleration of the automobile.

Answer to Problem 106A

  $11{\text{ m/s}}^{\text{2}}$

Explanation of Solution

Given:

Change in speed of automobile, $\Delta v=112$m/s

Elapsed time, $\Delta t=9.8$ s.

Formula used:

  $\overline{a}=\frac{\Delta v}{\Delta t}$

where,

  Change in velocity

  Elapsed time

Calculation:

Substitute the values in above formula and solve:

  $\begin{array}{c}\overline{a}=\frac{112}{9.8}\\ =11{\text{m/s}}^{\text{2}}\end{array}$

Conclusion:

Hence, the average acceleration of the automobile is $11{\text{ m/s}}^{\text{2}}$ .