An engineer is testing the impact resistance of a 3\text{ kg} structural component by rele… — Armed Services Vocational Aptitude Battery (ASVAB)

An engineer is testing the impact resistance of a $3\text{ kg}$ structural component by releasing it from rest in a drop tower. Ignoring air resistance and assuming the acceleration due to gravity is $9.8\text{ m/s}^2$ , what is the downward velocity of the component exactly $2\text{ seconds}$ after it is released?

A
$9.8\text{ m/s}$
$19.6\text{ m/s}$ Answer
C
$29.4\text{ m/s}$
D
$58.8\text{ m/s}$

Answer

The downward velocity of the component is

19.6\text{ m/s}

The velocity of an object in free fall starting from rest is determined by multiplying the acceleration due to gravity by the time elapsed (

v = gt

). Because air resistance is ignored, the

3\text{ kg}

mass is completely irrelevant to the fall speed. Multiplying

9.8\text{ m/s}^2

2\text{ seconds}

yields exactly

19.6\text{ m/s}

Step-by-Step Solution

Identify the given variables needed for the kinematic equation.

Initial velocity (

v_0

) =

0\text{ m/s}

, Acceleration (

g

) =

9.8\text{ m/s}^2

, Time (

t

) =

2\text{ s}

, Mass (

m

) =

3\text{ kg}

Extracting the knowns determines which formula is needed to find the final velocity.

Select the correct formula for velocity in free fall and eliminate irrelevant information.

v = v_0 + gt

. Mass (

3\text{ kg}

) is not needed.

All objects in free fall accelerate at the same rate regardless of their mass when air resistance is ignored.

Substitute the values and calculate the final velocity.

v = 0 + (9.8\text{ m/s}^2 \times 2\text{ s}) = 19.6\text{ m/s}

Multiplying the constant acceleration by the time elapsed gives the instantaneous velocity.

Key Concept

In the absence of air resistance, all objects fall with the same constant acceleration regardless of mass, and velocity is the product of this acceleration and time (

v = gt

Question

Answer

Step-by-Step Solution

Key Concept

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