A stunt car with a mass of 800\text{ kg} accelerates from rest to a speed of 20\text{ m/s}… — Armed Services Vocational Aptitude Battery (ASVAB)

A stunt car with a mass of $800\text{ kg}$ accelerates from rest to a speed of $20\text{ m/s}$ along a straight, level track. How much work is done by the net force to accelerate the car?

A
$8{}000\text{ J}$
B
$16{}000\text{ J}$
$160{}000\text{ J}$ Cevap
D
$320{}000\text{ J}$

Cevap

160{}000\text{ J}

According to the work-energy theorem, the net work performed on an object equals its change in kinetic energy (

W = \Delta KE

). Because the car accelerates from rest, its initial kinetic energy is zero. The final kinetic energy is calculated as

\frac{1}{2}mv^2 = \frac{1}{2}(800\text{ kg})(20\text{ m/s})^2 = 400 \times 400 = 160{}000\text{ J}

. Thus, the work done on the car is

160{}000\text{ J}

Adım Adım Çözüm

Apply the work-energy theorem to relate the net work done to the change in kinetic energy.

W = \Delta KE = KE_{\text{final}} - KE_{\text{initial}}

The net work done on an object equals the change in its kinetic energy.

Calculate the initial and final kinetic energy values.

KE_{\text{initial}} = 0\text{ J}

and

KE_{\text{final}} = \frac{1}{2}mv^2 = \frac{1}{2}(800\text{ kg})(20\text{ m/s})^2 = 400 \times 400 = 160{}000\text{ J}

The car starts from rest (

v_0 = 0\text{ m/s}

) and reaches a speed of

20\text{ m/s}

Determine the net work done on the car.

W = 160{}000\text{ J} - 0\text{ J} = 160{}000\text{ J}

Subtracting initial kinetic energy from final kinetic energy yields total work.

Anahtar Kavram

Work-Energy Theorem and Kinetic Energy Calculation

Tahmini Süre:1m 0s

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