An autonomous warehouse transport vehicle with a mass of 2,000 \text{ kg} experiences a co… — Armed Services Vocational Aptitude Battery (ASVAB)

An autonomous warehouse transport vehicle with a mass of $2,000 \text{ kg}$ experiences a constant frictional resistance of $2,000 \text{ N}$ while moving across a level concrete floor. When its electric motors produce a forward thrust of $6,000 \text{ N}$ , the vehicle accelerates at a steady rate. If the motors are commanded to double their forward thrust to $12,000 \text{ N}$ while the frictional resistance remains unchanged, what is the vehicle's new acceleration?

A
$4.0 \text{ m/s}^2$
$5.0 \text{ m/s}^2$ Answer
C
$6.0 \text{ m/s}^2$
D
$0.5 \text{ m/s}^2$

Answer

The new acceleration is

5.0 \text{ m/s}^2

According to Newton's Second Law, acceleration is determined by the net force acting on an object (

a = \frac{F_{net}}{m}

). The net force is the forward thrust minus the friction. With a new thrust of

12,000 \text{ N}

and a constant friction of

2,000 \text{ N}

, the net force is

10,000 \text{ N}

. Dividing this by the mass of

2,000 \text{ kg}

yields an acceleration of

5.0 \text{ m/s}^2

Step-by-Step Solution

Identify the forces acting on the vehicle in the new scenario.

Forward thrust (

F_{thrust}

) =

12,000 \text{ N}

. Frictional resistance (

F_{friction}

) =

2,000 \text{ N}

Newton's Second Law requires the net force, which is the sum of all opposing forces.

Calculate the new net force.

F_{net} = 12,000 \text{ N} - 2,000 \text{ N} = 10,000 \text{ N}

The net force is the actual force available to accelerate the mass.

Apply Newton's Second Law (

F = ma

) to find the new acceleration.

a = \frac{F_{net}}{m} = \frac{10,000 \text{ N}}{2,000 \text{ kg}} = 5.0 \text{ m/s}^2

Acceleration is equal to the net force divided by the mass.

Key Concept

Acceleration is directly proportional to the net force, not just the applied force. To find acceleration, all opposing forces must be subtracted from the applied force before dividing by mass.

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