Finding Velocity and Displacement

[BlackMamba]

My problem states: A speedboat starts from rest and accelerates at +2.01 m/s^2 for 7.25s. At the end of this time, the boat continues for an additional 6.05s with an acceleration of +0.518 m/s^2. Following this, the boat accelerates at -1.49 m/s^2 for 8.05s.

(a) What is the velocity of the boat at t = 21.35s?

(b) Find the total displacement of the boat.


So here was my thinking. The boat was speeding up during the first two stages and slowing down during the third. t = 21.35s is nothing more than the three time intervals given in the question added together. So couldn't I just find the velocity for each time interval and then add them together? At least that's what I tried to do, and my answer was incorrect. I was having trouble discerning what the starting velocity would be for the last two intervals as the first one is clearly 0m/s.

I'm assuming also that once I've found the velocity at t = 21.35s. I will be able to use that to find the total displacement.

 

[Tide]

It doesn't work that way. You have to treat each interval separately.

 

[BlackMamba]

Right, I suspected that. So even if I found the velocities of each time interval and added them together, that wouldn't give me the velocity of t = 21.35s.?

 

[Tide]

Nope! You're just going to have to do it!

 

[BlackMamba]

Do what?! LOL Obviously, I have no idea what I'm doing. So I find the velocities of each interval, then what??

 

[Tide]

Find the velocities AND the distances for each interval. Use the velocity and position for each interval as the starting conditions for the next interval. Then you're done! :-)

 

[BlackMamba]

Alright. I liked my initial way of doing things better. LOL

 

[Tide]

Yes, but just think of all fun you'll have on the journey!

 

[BlackMamba]

Well I'll admit, it wasn't as bad as I thought it would be.