A motorized winch pulls a cable, accelerating a load from rest (0\text{ m/s}) to a final v… — Armed Services Vocational Aptitude Battery (ASVAB)

A motorized winch pulls a cable, accelerating a load from rest ( $0\text{ m/s}$ ) to a final velocity of $18\text{ m/s}$ in $6\text{ seconds}$ at a constant rate. What is the acceleration of the load in meters per second squared ( $\text{m/s}^2$ )?

Answer: 3 m/s^2

Answer

The acceleration of the load is

3\text{ m/s}^2

Acceleration is calculated by dividing the total change in velocity by the elapsed time (

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

). Because the load accelerates uniformly from

0\text{ m/s}

18\text{ m/s}

over

6\text{ s}

, the acceleration is

\frac{18\text{ m/s} - 0\text{ m/s}}{6\text{ s}} = 3\text{ m/s}^2

Step-by-Step Solution

Identify the initial velocity, final velocity, and elapsed time from the given problem.

v_i = 0\text{ m/s}

v_f = 18\text{ m/s}

, and

t = 6\text{ s}

These parameters are required to calculate uniform linear acceleration.

Set up the acceleration formula:

a = \frac{\Delta v}{t} = \frac{v_f - v_i}{t}

a = \frac{18 - 0}{6}

Acceleration represents the rate of change of velocity with respect to time.

Perform the division to compute the numerical value.

a = 3\text{ m/s}^2

Dividing

18\text{ m/s}

6\text{ s}

yields

3\text{ m/s}^2

Key Concept

Linear acceleration is defined as the change in velocity divided by the time interval over which the change occurs (

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

Estimated Time:45s

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Key Concept

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