During a runway clearing operation, an armored recovery vehicle pushes a disabled transpor… — Armed Services Vocational Aptitude Battery (ASVAB)

During a runway clearing operation, an armored recovery vehicle pushes a disabled transport truck horizontally across the tarmac. The truck has a weight of $80,000 \text{ N}$ . The recovery vehicle applies a forward force of $30,000 \text{ N}$ , while the truck's damaged axles create a constant rolling resistance of $10,000 \text{ N}$ . Assuming the acceleration due to gravity is $10 \text{ m/s}^2$ , what is the forward acceleration of the disabled truck?

A
$3.75 \text{ m/s}^2$
B
$0.4 \text{ m/s}^2$
$2.5 \text{ m/s}^2$ Answer
D
$0.25 \text{ m/s}^2$

Answer

The disabled truck will have a forward acceleration of

2.5 \text{ m/s}^2

The correct acceleration is found by first converting the truck's weight to its mass, determining the net force by subtracting the rolling resistance from the applied force, and then dividing that net force by the mass.

Step-by-Step Solution

Calculate the mass of the truck from its weight.

m = \frac{80,000 \text{ N}}{10 \text{ m/s}^2} = 8,000 \text{ kg}

Newton's Second Law requires mass, not weight, to calculate acceleration.

Determine the net force acting on the truck.

F_{net} = 30,000 \text{ N} - 10,000 \text{ N} = 20,000 \text{ N}

The rolling resistance directly opposes the applied forward force, so it must be subtracted.

Calculate the acceleration using Newton's Second Law (

F = ma

a = \frac{F_{net}}{m} = \frac{20,000 \text{ N}}{8,000 \text{ kg}} = 2.5 \text{ m/s}^2

Acceleration is directly proportional to net force and inversely proportional to mass.

Key Concept

Applying Newton's Second Law (

F=ma

) in multi-force scenarios requiring weight-to-mass conversion.

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