Solve Kinematics: Find Velocity & Displacement of Speedboat

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The speedboat accelerates in three stages: first at +2.03 m/s² for 8.87 seconds, then at +0.380 m/s² for 8.86 seconds, and finally decelerates at -1.20 m/s² for 8.11 seconds. The calculated velocity at 25.84 seconds is 7.28 m/s. The total displacement requires integrating the velocity over time, which can be visualized using a velocity-time diagram to find the area under the curve. Assistance is needed to calculate the total displacement accurately. Understanding the integration of velocity over time is crucial for solving the displacement part of the problem.
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Homework Statement



A speedboat starts from rest and accelerates at +2.03 m/s2 for 8.87 s. At the end of this time, the boat continues for an additional 8.86 s with an acceleration of +0.380 m/s2. Following this, the boat accelerates at -1.20 m/s2 for 8.11 s. (a) What is the velocity of the boat at t = 25.84 s? (b) Find the total displacement of the boat.

Homework Equations


The equations to be used are :
v= u + at
s= ut + 1/2 at^2

The Attempt at a Solution



i understand that you use the above equations to work through each stage in the speedboats journey:
stage 1: v=11.69m/s
s=40.23m
stage 2: using the previous velocity
v=16.47m/s
s=102.236 m
stage 3: using the previous velocity
v= 7.28
s= 100.11

so the solution is velocity at 25.84 seconds is 7.28 m/s that part of my working is correct, what i don't understand is how to find the total displacement, please help
 
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