Question

Consider a car of mass m with initial velocity v. The car is brought to rest by applying a constant force F in the opposite direction of motion. Which of the following equations represents the relationship between the force F, mass m, initial velocity v, and final velocity u?

1) F = m(v - u)
2) F = m(u - v)
3) F = mv
4) F = mu

Answer 1

The correct equation that represents the relationship between force F, mass m, initial velocity v, and final velocity u for a car coming to rest is F = m(v - u), which agrees with Newton's second law of motion.

Step-by-step explanation:

The relationship between the force F, mass m, initial velocity v, and final velocity u for a car being brought to rest by applying a constant force is described by Newton's second law of motion, which states that force is equal to mass times acceleration (F = ma). Since the car is coming to rest, the final velocity u is 0 m/s, and the initial velocity is v. The acceleration can then be calculated by rearranging the formula to a = F/m. Using v = u + at (where u is the final velocity, a is the acceleration, and t is the time), and since u is 0, we can deduce the correct equation as F = m(v - u). Option 1 reflects this, as it takes into account the direction of the force opposing the initial motion.