05. A Different Model

A Different Model

More Complex Motion

Now, what if I gave you a more complex motion example?

And I told you that our car starts at the same point, at the 0m mark, and it’s moving 50m/s forward, but it’s also slowing down at a rate of 20m/s^2. This means it’s acceleration = -20m/s^2.

Car moving at 50m/s and slowing down over time.

Car moving at 50m/s and slowing down over time.

Acceleration

So, if the car has a -20 m/s^2 acceleration, this means that:

  • If the car starts at a speed of 50m/s
  • At the next second, it will be going 50-20 or 30m/s and,
  • At the next second it will be going 30-20 or 10m/s.

This slowing down is also continuous, which means it happens gradually over time.

New Model, New State

For the next two quizzes, I want you to keep in mind this question: Where will the car be after 3 seconds?

I also want to ask you:

  • What variables do you need to solve this problem? In other words, what values should be included in the state? And…
  • What motion model should we use to solve this problem?

State variables

What variables do you need to solve the localization question above? In other words, what values should be included in the state?
SOLUTION:
  • current position
  • velocity
  • acceleration

Motion Model 1

What piece of a motion model fits this scenario?
SOLUTION: `change in velocity = acceleration*time`

Predicting state 2

Where do you think the car will be after three seconds have elapsed? And what will it's velocity be?
SOLUTION: x = 60m, vel = -10m/s

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