Suppose that a box is accelerating at a rate of 4 m/s2. If the net force is tripled and the mass is doubled, then what is the new acceleration of the box?

6m/s2

Explanation: Recall, F =ma

a =F/m

Where a = 4m/s2

So, 4 =F/m equation ( 1)

Now we shall see the value of a where 3F and 2m

Thus,

a =F/m

a = 3F/2m

a =3/2 ×F/m equation ( 2 )

Now, substitute equation 1 into 2

F/m = 4

a =3/2 ×4

a = 12/2

a = 6m/s2

The new acceleration of the box = 6 m/s²

That is, 1.5 of the old acceleration.

Explanation:

Acceleration of the box = 4 m/s²

From Newton's law, F = ma

F = 4m (eqn 1)

Then the force is tripled, that is, New force, F₁ = 3F

the mass is doubled, New mass, m₁ = 2m

This will produce new acceleration, a₁

Still consistent with Newton's law

New force = New mass × New acceleration

F₁ = m₁ × a₁

3F = 2m × a₁

a₁ = 3F/(2m)

But from eqn 1

F = 4m

a₁ = 3(4m)/2m = 3×4/2 = 6 m/s²

Hence the new acceleration = 6 m/s²

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