Final answer:
The maximum velocity during the journey is 15 m/s and the total displacement is 37.5 m.
Step-by-step explanation:
To find the maximum velocity during the journey, we need to divide the journey into two parts: the first part where the body is accelerating and the second part where the body is decelerating.
During the accelerating phase, the body starts from rest and has a uniform acceleration of 3 m/s². Since the total time of the journey is 10 seconds, the time taken for the accelerating phase is t = 10/2 = 5 seconds.
Using the formula v = u + at, where v is the final velocity, u is the initial velocity (which is 0), a is the acceleration, and t is the time, we can calculate the maximum velocity during the accelerating phase: vmax = 0 + 3 * 5 = 15 m/s.
To find the total displacement, we need to find the distance traveled during the accelerating phase and the decelerating phase. Using the formula s = ut + (1/2)at², where s is the displacement, u is the initial velocity (which is 0), a is the acceleration, and t is the time, we can calculate the distance traveled during the accelerating phase: s = 0 * 5 + (1/2) * 3 * (5)² = 37.5 m.
Since the body comes to rest during the decelerating phase, the distance traveled during the decelerating phase is 0.
Therefore, the total displacement is the sum of the distances traveled during the accelerating and decelerating phases: total displacement = 37.5 + 0 = 37.5 m.