Question

for a moving object, the force acting on the object varies directly with the objects acceleration. when a force of 14 n acts on a certain object, the acceleration of the object is 2 m/s². if the force is changed to 63 n, what will be the acceleration of the object?

Explanation:

Step1: Establish the proportional - relationship

Since force $F$ varies directly with acceleration $a$, we have $F = ka$, where $k$ is the constant of proportionality. When $F = 14$ N and $a=2$ m/s², we can find $k$. Substituting into the equation $14 = k\times2$, then $k=\frac{14}{2}=7$ N·s²/m.

Step2: Calculate the new acceleration

Now that we know $k = 7$ N·s²/m and the new force $F = 63$ N. Using the equation $F=ka$ and solving for $a$, we get $a=\frac{F}{k}$. Substituting $F = 63$ N and $k = 7$ N·s²/m into the formula, we have $a=\frac{63}{7}=9$ m/s².

Answer:

9 m/s²