A light training aircraft with a mass of 750\text{ kg} accelerates from rest along a strai… — Armed Services Vocational Aptitude Battery (ASVAB)

A light training aircraft with a mass of $750\text{ kg}$ accelerates from rest along a straight runway under a constant net forward force of $1{}500\text{ N}$ . What is the velocity of the aircraft, in meters per second ( $\text{m/s}$ ), after $8\text{ seconds}$ ?

Answer: 16 m/s

Answer

16 m/s

According to Newton's second law (

F = ma

), a net force of

1{}500\text{ N}

applied to a mass of

750\text{ kg}

produces a constant acceleration of

a = \frac{1{}500}{750} = 2\text{ m/s}^2

. Starting from rest (

v_0 = 0

), the velocity after

8\text{ seconds}

v = at = 2\text{ m/s}^2 \times 8\text{ s} = 16\text{ m/s}

Step-by-Step Solution

Calculate the constant acceleration of the aircraft using Newton's second law of motion (

F_{\text{net}} = ma

a = \frac{1{}500\text{ N}}{750\text{ kg}} = 2\text{ m/s}^2

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

Calculate the final velocity after

8\text{ seconds}

using the kinematic equation for uniform acceleration (

v = v_0 + at

v = 0\text{ m/s} + (2\text{ m/s}^2)(8\text{ s}) = 16\text{ m/s}

Starting from rest, the final velocity equals the constant acceleration multiplied by elapsed time.

Key Concept

Newton's Second Law and Uniform Acceleration

Alternative Method

Apply the impulse-momentum theorem:

\text{Impulse} = F_{\text{net}} \times \Delta t = \Delta p = m \times v

. Solving for velocity gives

v = \frac{F_{\text{net}} \times \Delta t}{m} = \frac{1{}500\text{ N} \times 8\text{ s}}{750\text{ kg}} = \frac{12{}000}{750} = 16\text{ m/s}

Estimated Time:1m 0s

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