I want to apologize if you think my question is a duplicate but honestly I could not understand the answer I found in this question, nor any other answer I found on from searching.
I have a robot that should start decelerating when it's ultrasonic sensor starts giving values below 70 (assuming it's cm), this deceleration should continue until it reaches 35 cm. my initial velocity is a variable but for now we could assume it is 48.8793 cm/s. I want to be able calculate required amount of deceleration so when I reach 35 cm I know for sure my velocity is 23 cm/s.
Again I'm sorry if my question is a duplicate I've been just confusing myself for the past couple of days, also my tags might be referring to unrelated areas? would appreciate any help.
Thank you
/y
We do the calculation, describing in some detail the reasoning.
Let the velocity when the sensor reads $70$ cm be $v_0\gt 23$.
We will apply a constant acceleration $-a$ (the minus sign is because we are decelerating).
Let $t$ be the amount of time we take to get from sensor says $70$ to sensor says $35$.
The end-velocity is $23$.
We have $$at=v_0-23.\tag{1}$$
For the acceleration times elapsed time is the change in velocity.
The average velocity from the time we start decelerating to the end is $\dfrac{v_0+23}{2}$. At this average velocity, we travelled a net distance of $70-35=35$ in time $t$. Thus $$35=\frac{v_0+23}{2}{t}.\tag{2}$$ We want to use Equations 1 and 2 to eliminate $t$. Using the two equations, we get $$t=\frac{v_0-23}{a}=\frac{70}{v_0+23}.$$ This can be rewritten as $$a=\frac{v_0-23}{70(v_0+23)}.$$