Question

For a moving object, the force acting on the object varies directly with the object's acceleration. When a force of 40 N acts on a certain object, the acceleration

of the object is 8 m/s². If the force is changed to 45 N, what will be the acceleration of the object?
m/s²
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3

I need this now 50 points

Answer 1

see below

Explanation:

we are here given that Force varies directly with the object's acceleration. that is ;

F ∝ a

F = ka [ k is a constant]

Now, when

• F = 40N
• a = 8m/s²

so ,

40N = k * 8m/s²

k = 40N/8ms-²

k = 5kg

again in second case,

• F = 45N
• a = ?

substitute the respective values of F and k,

45N = a * 5kg

a = 45N/5kg

a = 9m/s²

Hence the required answer is 9m/s².

And we are done!

Answer 2

9 m/s²

Explanation:

Define the variables:

• Let F be the force acting on the object (in Newtons).
• Let a be the acceleration of the object (in m/s²).

If the force acting on the object varies directly with the object's acceleration:

`\boxed{F \propto a \implies F=ka}`

(where k is a constant).

Given F = 40 N when a = 8 m/s². Substitute these values into the equation and solve for k:

`\implies 40=8k`

`\implies k=(40)/(8)`

`\implies k=5`

Therefore, the equation that models the given scenario is:

`\boxed{F=5a}`

If the force is changed to 45 N, substitute F = 45 into the equation and solve for a:

`\implies 45=5a`

`\implies a=(45)/(5)`

`\implies a=9\; \sf m/s^2`

Therefore, the acceleration of the object when the force is 45 N is:

• 9 m/s²