Final answer:
The correct answer for how much time t it takes for a mass m to move a distance x when pushed with a constant force f, starting at rest, is √(2mx/f), which is option b. This is derived using the second equation of motion and Newton's second law of motion.
Step-by-step explanation:
The question asks how much time t it takes for a mass m starting at rest to move a distance x when pushed with a constant force f. By using the second equation of motion which is derived from the kinematic equations, s = ut + ½at² (where s is the displacement, u is the initial velocity, a is the acceleration, and t is the time), we can solve for the time t. Since the body starts from rest, u = 0, and the force f is related to acceleration a by Newton's second law f = ma. Therefore we have:
x = ½at²
By substituting a = f/m we get:
x = ½(f/m)t² => 2x = (f/m)t² => t² = (2mx/f)
So, the time t is:
t = √ (2mx/f)
This corresponds to option b on the list.
Regarding the kinematic equations example, the correct answer to the given practice problems would be:
a. A body starts from rest and accelerates at 4 m/s² for 2 s. The body's final velocity is 8 m/s - correct by using the equation v = u + at.
c. A body with a mass of 2 kg is acted upon by a force of 4 N. The acceleration of the body is 2 m/s² - correct by using the equation f = ma.
b. The force F on an object is equal to its mass m multiplied by its acceleration a. If a wagon with mass 55 kg accelerates at a rate of 0.0255 m/s², the force on the wagon is 1.4025 N.