Solving for Displacement: 9.8m or 36m?

[IWillBarelyUseThis]

Homework Statement

Don't have exact wording, but the basics are this: A man steals a purse and runs across the field at 5.5m/s. A nearby woman sees this, and while the man passes her, she begins accelerating at 2.5m/(s^2) after him. She reaches her maximum speed of 7.0m/s as she catches the robber. What is her displacement from where she started?

It was multiple choice, and though I don't remember all the answers, I remember that 36m was the correct one, and that my answer of 9.8m was not an option.

Relevant Equations

The equations that I tried led to an answer that wasn't an option, and the teacher said it was entirely wrong, but it was essentially (final velocity squared - initial velocity squared) / (2 × acceleration) = displacement. Basic rearranging of an equation on the formula sheet.

So the equation I had used made sense to me because through the wording of the question, since we have an initial velocity of 0m/s, and an acceleration of 2.5m/(s^2), and it was implied in the question that she caught the robber at the exact same time as she reached her maximum velocity, and therefore also final velocity. I plugged the values into the equation, given to us on a formula sheet, and solved for displacement, which was 9.8m. Of course, that wasn't one of the answers, and her explanation made no sense. Along with that- she also said that her explanation would NOT make sense to us unless we were in her physics 20 class last semester. Now, I took that class last year, meaning I didn't have her as a teacher, and don't understand what her explanation was, but that's a lazy excuse to explain why your students don't know what you're doing. It means you aren't teaching them properly for starters, and more importantly, neither of the other two people in my group knew what she was talking about either. (And both of them were in the class last semester). So, assuming my answer is incorrect, and the question ISN'T worded as poorly as I think it is, how would I go about finding this value of 36m?

 

[IWillBarelyUseThis]

I would also like to clarify, yes I know the answer I got is incredibly small to make any sense, but it was spat out of an equation that makes sense in the context, so I didn't question it too much. Also I'm a bit rusty of physics, since It's been over a year and a few months since I've had to do any of this, and I didn't retain a lot of memory from the earlier parts of physics.

 

[haruspex]

The difficulty is that there is inconsistent information provided, so the answer you get will depend on which data you choose to ignore.
Your method was valid, and it ignored the 5.5m/s. Try ignoring each of the other figures in turn and see which results match an option.

 

[rsk]

I agree that the question as you've written it here is inconsistent. If I had to choose which bit of info to ignore it would be the 5.5 m/s of the man, because maybe to assume he runs at constant speed is incorrect.

If you can find the actual wording, we can have a go at working out how to get the 36m. In the absence of that, I'd have done exactly what you did and got the same answer.

My first idea was to take the man running at constant speed, write equations for the displacement of each and equate them to solve for t, then subs back for displacement. But in this case that does not give a correct answer and does not have her running at 7.0 m/s when she catches him. (That's pretty fast anyway...)

 

[256bits]

As per @rsk , one can ask:
How many seconds have passed from her start at 0m/s to 7m/s?
How far has she traveled in that time?
How far has he traveled in that time?

 

[IWillBarelyUseThis]

As per @rsk , one can ask:
How many seconds have passed from her start at 0m/s to 7m/s?
How far has she traveled in that time?
How far has he traveled in that time?

Yeah, that was what I figured, but the issue was with the improper grammar of the question. It DOES specifically say "The girl reaches her maximum speed of 7.0m/s as she catches the robber", but that obviously can't be true for the intended answer to the question. I think I have a better idea of how to do it now, but the fact that she said her answer could only be understood if I was there last semester, and then outright denies its improper phrasing, is more what had me frustrated by it.

 

[rsk]

You are exactly correct - if we say she reaches 7.0m/s and then carries on, it works and the answer is 36m

You said in the first post that you didn't understand her explanation so forgive me for this if you've already got this solved now

Let's say she catches him at time t after he passes her.

We work out how long it takes her to accelerate to 7.0m/s (2.8s) and how far she runs in this time (9.8m) and that in the remaining time she runs a further 7(t - 2.8)m.

So now we know that
9.8 + 7 x (t - 2.8) = 5.5 x t

Solving for t and subs-ing back in gives 36m.

You are absolutely right, to say "as she catches him" is an appalling way to describe this! Far better would be that she reaches this speed and then continues UNTIL she catches him.