To calculate the distance traveled in the third of the journey, we need to make a few assumptions. Let's assume the object starts from rest (initial velocity, vᵢ = 0) and travels a total distance of d.
The average velocity during uniform acceleration can be calculated using the formula:
v_avg = (vᵢ + v_f) / 2
In this case, since the object starts from rest, the average velocity simplifies to:
v_avg = v_f / 2
The final velocity (v_f) can be calculated using the equation of motion:
v_f = vᵢ + a * t
Since the object starts from rest, vᵢ = 0, and the equation simplifies to:
v_f = a * t
where a is the constant acceleration and t is the time.
Now, the distance traveled (d) can be calculated using the formula:
d = vᵢ * t + (1/2) * a * t^2
However, we need to determine the time (t) for the third of the journey.
Let's say the total time for the journey is T. Then, the time for the third of the journey (t_third) can be calculated as:
t_third = T / 3
Now we can substitute the values into the equations.
For the final velocity:
v_f = a * t_third
For the distance traveled in the third of the journey:
d_third = (1/2) * a * t_third^2
Substituting t_third = T / 3, we have:
d_third = (1/2) * a * (T / 3)^2
Simplifying further:
d_third = (1/2) * a * (T^2 / 9)
Therefore, the distance traveled in the third of the journey is (1/2) * a * (T^2 / 9), where a is the constant acceleration of 10 m/s^2 and T is the total time of the journey.