Question

For a moving object, the force acting on the object varies directly with the objects acceleration. When a force of 35 N acts on a certain object, the acceleration of the object is 5 m/s^2. If the force is changed to 21 N, what will be the acceleration of the object?

Answer 1

Answer: 3 m/s^2

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According to Newton's Second Law, we know that

F = m*a

where F is the force applied, m is the mass and 'a' is the acceleration.

We see that this is a direct variation equation for F and a, such that m is the constant of variation. It's similar to how y = kx is also a direct variation equation.

Plug in F = 35 and a = 5 to find m

F = ma

35 = m*5

35/5 = m

7 = m

m = 7

The object has a mass of 7 kg

Our equation F = ma updates to F = 7a

Now plug in the force F = 21 to find 'a'

F = 7a

21 = 7a

21/7 = a

3 = a

a = 3

The acceleration will be 3 m/s^2

Notice how a smaller force applied means that the acceleration has also gone down as well.