Four mobile systems are evaluated during performance trials on a flat testing course. Arra… — Armed Services Vocational Aptitude Battery (ASVAB)

Four mobile systems are evaluated during performance trials on a flat testing course. Arrange the systems in order of their kinetic energy, from least to greatest.

1A $500\text{ kg}$ cargo transport moving at $4\text{ m/s}$
2A $10\text{ kg}$ automated inspection rover moving at $30\text{ m/s}$
3A $40\text{ kg}$ tracked reconnaissance unit moving at $20\text{ m/s}$
4A $2\text{ kg}$ calibration projectile moving at $100\text{ m/s}$

Answer

From least to greatest kinetic energy: the

500\text{ kg}

cargo transport (

4{}000\text{ J}

), the

10\text{ kg}

automated inspection rover (

4{}500\text{ J}

), the

40\text{ kg}

tracked reconnaissance unit (

8{}000\text{ J}

), and the

2\text{ kg}

calibration projectile (

10{}000\text{ J}

Applying the kinetic energy formula

KE = \frac{1}{2}mv^2

to each system yields

4{}000\text{ J}

for the

500\text{ kg}

transport at

4\text{ m/s}

4{}500\text{ J}

for the

10\text{ kg}

rover at

30\text{ m/s}

8{}000\text{ J}

for the

40\text{ kg}

unit at

20\text{ m/s}

, and

10{}000\text{ J}

for the

2\text{ kg}

projectile at

100\text{ m/s}

. Arranging these values from smallest to largest produces the correct sequence.

Step-by-Step Solution

Identify the formula for kinetic energy.

KE = \frac{1}{2}mv^2

, where

m

is mass in kilograms and

v

is velocity in meters per second.

Kinetic energy is directly proportional to mass and proportional to the square of velocity.

Calculate the kinetic energy for each of the four systems.

Cargo transport:

\frac{1}{2}(500)(4^2) = 250 \times 16 = 4{}000\text{ J}

; Inspection rover:

\frac{1}{2}(10)(30^2) = 5 \times 900 = 4{}500\text{ J}

; Reconnaissance unit:

\frac{1}{2}(40)(20^2) = 20 \times 400 = 8{}000\text{ J}

; Calibration projectile:

\frac{1}{2}(2)(100^2) = 1 \times 10{}000 = 10{}000\text{ J}

Quantitative values allow direct comparison across all systems.

Arrange the resulting energy values in ascending sequence.

4{}000\text{ J} < 4{}500\text{ J} < 8{}000\text{ J} < 10{}000\text{ J}

Orders the systems from least kinetic energy to greatest kinetic energy as required.

Key Concept

Kinetic energy is calculated as

KE = \frac{1}{2}mv^2

, meaning velocity has a quadratic effect compared to the linear effect of mass.

Estimated Time:1m 30s

Question

Answer

Step-by-Step Solution

Key Concept

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