Final answer:
To double the acceleration of a given mass, you must apply twice the force, as dictated by Newton's second law of motion, Fnet = ma.
Step-by-step explanation:
In order to get the same mass accelerating twice as much, you need twice as much force. This stems from Newton's second law of motion which is often formulated as Fnet = ma, where Fnet stands for the net force applied to an object, m denotes the mass of the object, and a represents the acceleration.
Therefore, if you want to double the acceleration (2a) while keeping the mass (m) the same, the equation shows that the net force must also be doubled, becoming 2F.
For example, if a car requires 100 N to accelerate at 5 m/s², applying a force of 200 N would accelerate the car at 10 m/s², assuming no other forces like friction are altering the result.
According to Newton's second law, force (F) is directly proportional to mass (m) and acceleration (a). So, if the mass is accelerating twice as much, you would need twice as much force to achieve that acceleration. For example, if you have an object with a mass of 1 kg and it is accelerating at 2 m/s^2, you would need a force of 2 newtons. If you want the same mass to accelerate at 4 m/s^2, you would need a force of 4 newtons.