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paulb203

Member

Registered: 2023-02-24

Posts: 374

Velocity Time graphs

A mouse is trying to cross the street. Its velocity
\[v\] as a function of time
\[t\] is given in the graph below where rightwards is the positive velocity direction.
A set of black coordinate axes are given with the vertical axis labeled "v (m/s)" and the horizontal axes labeled "t (s)".  A curve that relates v to t is shown in blue.  It begins with a straight line of endpoints (0,0) and (1,5). This first line is connected to a second line with endpoints (1,5) and (3,-5). This second line is then connected to a third line of endpoints (3,-5) and (6,-5). 
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{1}\]
\[\small{2}\]
\[\small{3}\]
\[\small{4}\]
\[\small{5}\]
\[\small{\llap{-}2}\]
\[\small{\llap{-}3}\]
\[\small{\llap{-}4}\]
\[\small{\llap{-}5}\]
\[v~(\text{m/s})\]
\[t~(\text s)\]
At what time does the mouse have the same position as
\[t = 0\,\text s\]?
Assume the motion is restricted to one dimension. Answer with two significant digits.

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,701

Re: Velocity Time graphs

hi paulb203

Here's the graph:

Below your descriptive paragraph is some code that isn't displaying usefully for me.  Also there are bits here that don't make sense for me. 

rightwards is the positive velocity direction.

But v is the up axis.

And what is this mouse doing? It starts with zero velocity and over a period of one second accelerates to 5 m/s. Then, in another second it decelerates back to zero at (2,0). It continues to accelerate negatively (ie accelerate but in the opposite direction) for another second and then continues at a steady speed for 3 more seconds.

By using 'area under the graph = distance travelled' I can see it has travelled 5 metres after 2 seconds.  But then the areas are negative so it's coming back from its original direction. -5 metres occurs at 4.5 seconds when it is back where it started?? Then it continues in that negative direction until 6 seconds by which time it has travelled 5 x 2.5 metres in the negative direction.  Has it crossed the road? Only if it was pointing the wrong way to start with and ran the wrong way until 4.5 seconds.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 374

Re: Velocity Time graphs

Thanks, Bob.

And, sorry, I didn't think I had submitted this one. I previewed it, saw all the code, and realised I don't know how to post an image on here (so I posted a thread on how to post images/photos) and thought I'd abandoned this post. Doh!

Anyway. Here is the question without all the code;

At what time does the mouse have the same position as t=0s?

I worked it out, eventually (3.5s). Did you get 4.5s?

It was the part, “...where rightwards is the positive velocity direction,” that had me puzzled.
Just to double check I’ve now got that;
Does it mean; when the velocity is positive, the displacement is to the right (and therefore, when the v is negative, the displacement is to the left)?

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Prioritise. Persevere. No pain, no gain.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,701

Re: Velocity Time graphs

Whoops, I did mean 3.5.  I just counted squares along the graph and miscounted.  Hey! I'm a mathematician; can't be bothered with all that counting business.

The velocity rightwards makes no sense at all since the velocity axis is up/down.

Here's my interpretation of the graph.

A mouse wants to cross the road and is waiting at the kerb. A big lorry thunders along and the mouse is so frightened it accelerates rapidly away from the road; then decelerates at the same magnitude; coming to rest after two seconds.  As the lorry has now passed the mouse continues the same acceleration back to the road; at t=3 it maintains the constant velocity it has reached of magnitude 5 m/s and 0.5 s later arrives back at the kerb. It continues with that velocity and crosses the road without mishap; arriving at the other side at t=6.

To achieve this interpretation the positive velocity is upwards and represents velocities away] from the road. The road is 12.5 metres wide.

Odd question but maybe in mouse kinetics it makes more sense.  Mice do spend a lot of their time running away from danger so they would take 'away' as the positive direction. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

paulb203

Member

Registered: 2023-02-24

Posts: 374

Re: Velocity Time graphs

Thanks, Bob.

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Prioritise. Persevere. No pain, no gain.