Question

for a moving object, the force acting on the object varies directly with the object’s acceleration. when a force of 24 n acts on a certain object the object is 8 \\(\frac{m}{s^2}\\). if the force is changed to 18 n, what will be the acceleration of the object?

Explanation:

Step1: Define direct variation relation

$F = ka$, where $F$ is force, $a$ is acceleration, $k$ is constant.

Step2: Solve for constant $k$

Substitute $F=24\ \text{N}$, $a=8\ \frac{\text{m}}{\text{s}^2}$:
$24 = k \times 8$
$k = \frac{24}{8} = 3$

Step3: Find new acceleration

Substitute $F=18\ \text{N}$, $k=3$ into $F=ka$:
$18 = 3 \times a$
$a = \frac{18}{3}$

Answer:

$6\ \frac{\text{m}}{\text{s}^2}$