Start with Newton's 2nd law of motion:
Force = (mass) x (acceleration) .
Since we're going to be talking about acceleration,
lets divide each side by (mass):
Acceleration = (force) / (mass) .
OK. We start out with a certain acceleration 'A₀'. It's the result of
a certain force 'F₀' and a certain mass 'M₀'. (I used the little subscripts " ₀ "
to show that these are the originals, before any changes.)
Original acceleration = (Original force) / (original mass)
A₀ = F₀ / M₀ .
Now you want to triple the force and cut the mass in half:
New acceleration A₁ = (3 F₀) / (1/2 M₀) .
Divide each side by 3: A₁ / 3 = F₀ / (1/2 M₀) .
Multiply each side by 1/2 : (1/2 A₁) / 3 = F₀/M₀
A₁ / 6 = F₀/M₀
Take a look at the right side of that equation . . . F₀/M₀ .
That's just the original acceleration A₀ .
So now, after the change, we have A₁ / 6 = A₀ .
You asked "What is the new acceleration ?"
OK. Multiply each side by 6 : A₁ = 6 A₀ .
Whatever the original acceleration was, the
new acceleration is 6 times as much.
If it was originally 2 m/s², then after the change, it becomes (6 x 2) = 12 m/s² .
