Question

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)

Answer 1

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 .