Suppose that a sled is accelerating at a rate of 2 m/s2. If the net force is tripled and the mass is halved, then what is the new acceleration of the sled?
(show how you solved it)
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 .
