Question

Consider the relationship of the variables in Newton’s second law. In a drag car race, the force applied to the car is doubled by the driver stepping on the gas pedal. The acceleration of the car will . The mass of the car will . The velocity of the car will .

Answer 1

When the driver mashes the gas, puts the pettle to the mettle, and doubles the engine force applied to the car . . .

-- the acceleration of the car doubles

-- the mass of the car doesn't change

-- the velocity of the car starts to increase in the direction in which the car is already moving. If the car's speed was already increasing forward before the force adjustment, then the rate at which it increases due to the doubled force will double.

Answer 2

Recall that the force on an object is related to the mass and acceleration of that object by the formula F = ma, where m is the mass of the object and a is its acceleration. What happens when we double F? Well, you might remember from algebra that, in order to keep our equality true, if we double one side, we must also double the other, so our equation becomes 2F = 2ma. Now, this means one of two things: either the mass has doubled, or the acceleration has doubled.

We can tell right away that it'd be absurd if a race car doubled in mass every time it hit the gas, so the quantity doubling must be the acceleration. If we call the car's current velocity v1, we'll be adding the doubled acceleration to get its new velocity. Mathematically, v = v1 + 2a.

We can now conclude that, by doubling the force:

• The acceleration of the car will double,
• The mass of the car will stay the same, and
• The velocity of the car will increase by double the original acceleration