For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 12 n acts on a certain object, the acceleration of the object is 3 m/s^2. If the acceleration of the object becomes 10 m/s^2, what is the force?
Let's denote the initial force as F1 and the initial acceleration as a1, and the final force as F2 and the final acceleration as a2.
From the given information:
F1 = 12 N
a1 = 3 m/s^2
a2 = 10 m/s^2
According to the relationship between force and acceleration:
F1 = k * a1
F2 = k * a2
where k is a constant of proportionality.
We can find the value of k by rearranging the equation F1 = k * a1 to get:
k = F1 / a1
k = 12 N / 3 m/s^2
k = 4 Ns^2
Now, use the value of k to find the force F2 when the acceleration is 10 m/s^2:
F2 = k * a2
F2 = 4 Ns^2 * 10 m/s^2
F2 = 40 N
Therefore, the force acting on the object when the acceleration is 10 m/s^2 is 40 N.