THE AREA UNDER A FORCE-TIME GRAPH REPRESENTS

• A. change in kinetic energy
• B. change in momentum ✓
• C. change in work done
• D. change in internal energy

The answer to the question is: B. change in momentum

The area under a force-time graph represents the change in momentum of an object. This is known as the impulse-momentum theorem, which states that the impulse on an object is equal to the change in its momentum. Impulse is defined as the product of the average force applied to an object and the duration of time that the force is applied. Mathematically, impulse (J) can be represented as:

J = F × ∆t

where F is the force and ∆t is the change in time. The change in momentum (∆p) of an object is then given by:

∆p = m × ∆v

where m is the mass of the object and ∆v is the change in velocity.

Since momentum (p) is defined as the product of mass and velocity (p = mv), when a constant force is applied to an object for a certain amount of time, it will cause a change in velocity, and hence a change in momentum.

The relationship between impulse and momentum can be derived from Newton’s second law of motion, which states that the force acting on an object is equal to the rate of change of its momentum. By integrating this relationship over time, we arrive at the impulse-momentum theorem.