Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 40 n acts on a certain object, the acceleration of the object is ( 4\frac{m}{s^2} ). if the force is changed to 70 n, what will be the acceleration of the object?

Explanation:

Step1: Define direct variation

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

Step2: Solve for constant $k$

Substitute $F=40$, $a=4$:
$40 = k \times 4$
$k = \frac{40}{4} = 10$

Step3: Find new acceleration

Substitute $F=70$, $k=10$:
$70 = 10a$
$a = \frac{70}{10}$

Answer:

$7 \frac{\text{m}}{\text{s}^2}$