Question

A body of mass m has initial velocity v₀ in the positive x-direction. It is acted on by a constant force F for time t until the velocity becomes zero; the force continues to act on the body until its velocity becomes −v₀ in the same amount of time. Write an expression for the total distance the body travels in terms of the variables indicated.

a) 2v0t
b) 4v0t
c) 3v0 t
d) 6v0t

Answer 1

The total distance traveled by the body can be found by summing the distances traveled during the two phases of motion: from the initial velocity to zero velocity, and from zero velocity to -v₀ velocity.

Step-by-step explanation:

The total distance traveled by the body can be found by summing the distances traveled during the two phases of motion: from the initial velocity to zero velocity, and from zero velocity to -v₀ velocity. During the first phase, the body is decelerating, so the distance traveled can be found using the formula:

distance1 = (v₀2) / (2a)

where v₀ is the initial velocity and a is the acceleration. Since the body reaches zero velocity, the acceleration can be found using:

a = -F / m

where F is the force applied and m is the mass of the body. During the second phase, the body is accelerating in the opposite direction, so the distance traveled can be found using the same formula with the velocity replaced by -v₀ and the acceleration replaced by -a. Therefore, the total distance traveled is:

total distance = distance1 + distance2