Calculate Constant Velocity & Speed for Trapezoid Move

[robertor]

Rounding

v = 24.59m/s OR v = 0.41m/s

I mean looking at it, I know which is more likely, is there a way to confirm which of these two values is correct?

 

[tiny-tim]

… looking at it, I know which is more likely, is there a way to confirm which of these two values is correct?

yup!

something comes out negative when it can't be

in most problems, you'd find that t₁ has one positive solution and one negative solution …

obviously, you reject the negative solution!​

but in this problem, it's slightly different …

can you see what it is? ​

 

[robertor]

I could calculate the displacement during t1, t2 and t3. They should add up to my known displacement, if they don't, then its the other one?

 

[tiny-tim]

no

what is the value of t₂ in each case? ​

 

[robertor]

Sure I can calculate the value of t₂ in this scenario, however my next task is to rewrite this equation as a generic formula to find t₁, using the same technique you have shown me. Therefore, sure I can look at t₂ in both cases but how will I know which one is correct. If I provide accel, decel, total time and total displacement, what happens if the object does not have time to accelerate to a constant velocity, and the shape within the velocity x time graph becomes a triangle? Surely t₂ could be negative using this current equation. There must be a more generic method for checking which value of V is correct, which is why I suggested adding up the displacements or the times to see if they equal the displacement or time provided at the beginning :)

 

[tiny-tim]

… which is why I suggested adding up the displacements or the times to see if they equal the displacement or time provided at the beginning :)

that can't possibly work: the correct values for total time and displacement were part of your input

Therefore, sure I can look at t₂ in both cases but how will I know which one is correct.

calculate both values, and then it should be obvious

what are they?​

 

[robertor]

Sure on this occasion the correct answer is obvious. However what I was pointing out is that the answer will not always be obvious, am I wrong?

 

[tiny-tim]

Sure on this occasion the correct answer is obvious. However what I was pointing out is that the answer will not always be obvious, am I wrong?

i'm not entirely convinced that you have got the correct answer, since you haven't specifically said what it is

the general rule is that if there's two solutions, then they're both valid …

why would they not be??​

the only exception is where something is undefined for particular values (in this case for negative values) of some variable

 

[robertor]

t₂

t₂ = 24.390079932 OR t₂ = -11.890079933

 

[tiny-tim]

yup! and, as i think you've noticed, t₂ can't be negative (unless you redefine the question considerably), so the second solution has to be rejected

(but plenty of problems do have two solutions, eg if you throw the ball at 5 m/s, at what angle should you throw it to get it through the hoop?)

 

[robertor]

What if both answers are positive?

 

[tiny-tim]

then both answers are valid