Question

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 9N acts on a certain object, the acceleration of the object is 3 m/s2 . If the force is changed to 6N , what will be the acceleration of the object?

Answer 1

The acceleration is 2m/s^2

Explanation:

Given

Variation: Direction Variation

Represent Force with F and Acceleration with A

When

`F= 9N; A=3m/s^2`

Required

Find A when F =6N

The variation can be represented as:

`F \alpha A`

Convert to an equation

`F = kA`

Where

`k = variation\ constant`

When

`F= 9N; A=3m/s^2`

We have:

`9N = k * 3m/s^2`

Solve or k

`k = (9N)/(3m/s^2)`

`k = 3kg`

When

`F = 6N`

We have:

`F = kA`

Substitute 6N for F and 3kg for k

`6N = 3kg * A`

Solve for A

`A = (6N)/(3kg)`

`A = 2m/s^2`