For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 50 N acts on a certain object, the acceleration of the object is 10 m/s^2 If the acceleration of the object becomes 8 m/s^2 what is the force?

Answer 1

Given that the force \( F \) acting on an object varies directly with its acceleration \( a \), we can express this relationship mathematically as:

\[ F = k \cdot a \]

where \( k \) is a constant of proportionality.

From the information given, when the force \( F \) is 50 N, the acceleration \( a \) is 10 m/s²:

\[ 50 = k \cdot 10 \]

To find \( k \), we can rearrange the equation:

\[ k = \frac{50}{10} = 5 \]

Now that we have determined \( k \), we can use it to find the force when the acceleration is 8 m/s². We substitute \( a = 8 \) into the equation:

\[ F = 5 \cdot 8 \]

Calculating this gives:

\[ F = 40 , \text{N} \]

Therefore, when the acceleration of the object becomes 8 m/s², the force acting on it is 40 N.