I have a boat traveling at 20 meters/second approaching destination x. Destination x has a range radius of 10 meters. What I would like to do is make sure by the time the boat arrives within 10 meters of destination x (i.e. boat gets to touch the orange circle) the boat speed is brought down to 5 m/s. The boat can decelerate at a rate of
I believe I need to first calculate the distance required to slow down to 5 m/s.
using the following equation of motion:
v^2 = u^2 + 2as
- v: final velocity
- u: initial velocity
- a: acceleration; -acceleration = deceleration
- s: displacement or distance
we can rearrange the variables in the formula above like so:
applying the following given variables:
- v = 5
- u = 20
- a = -0.5
s=(20^2-5^2)/(-2(-0.5)) = (400-25)/1 = 375
this means that at any moment of travel we need a distance of 375 meters to slow down from 20 m/s to 5 m/s. Now adding the fact that we need to slow down before we reach the circumference of the orange circle, we need to make sure we are at least 375 meters away.
Since we know location x, then we calculate distance from boat to
(x + 10 meters), call it d.
We check if
375 <= dthen we start to decelerate the boat?
Is the distance required to achieve speed 5 m/s while decelerating from 20 m/s is 375 meters?
Is my approach correct? Are my calculations correct?