M1 kinematics question

I have solved this problem, but one method produced a result which was impossible and which I can't give a good reason for it being impossible...

So the method that did not work: using S = vt - 0.5at^2

400 = 20t - 0.17t^2, 0.17t^2 - 20t + 400 = 0, solving by the quadratic formula gives: 58.8235 +/- 33.2756

Now the correct answer is 25.5~, i.e. 58.8 - 33.3. (also by my other method, finding initial velocity at A, then substituting into S = 0.5 (u+v) t)

So my question is, with the +/- answer, is there a way of saying 25.5 is the correct answer mathematically?

Normally it is easy to distinguish a correct answer mathematically in these sort of equations, as one is positive and one is negative, but due to both answers being positive it has confused me...

I know by using the other method I get a correct answer, but I'm just curious as to how I can't use another seemingly valid technique and mathematically state one result is correct.

Anywho, any help much appreciated. :smile:

JackF

...

This is rather a tricky little question for M1, IMHO. As stated, the other solution isn't impossible.

If you use

v^2=u^2+2as

on the whole interval, then you get

u = \pm8\sqrt{2}

.

If u is positive, then the mass is going directly from A to C, and this takes the shorter time.

If u is negative then initially the mass is travelling away from C, comes to a stand still (due to the +ve acceleration), and then starts travelling towards C, passing through A again (this time with velocity

+8\sqrt{2}

) and this takes the longer time.

So the question has some ambiguity, although there may be something in the exact wording of the question that allows you to distinguish between the two solutions.

From the English usage, I would assume it's going directly to C, but I wouldn't say the other solution is wrong.

The information about B is redundant.

Reply 2

BeefyCheese

JackF

I have solved this problem, but one method produced a result which was impossible and which I can't give a good reason for it being impossible...

So the method that did not work: using S = vt - 0.5at^2

400 = 20t - 0.17t^2, 0.17t^2 - 20t + 400 = 0, solving by the quadratic formula gives: 58.8235 +/- 33.2756

Now the correct answer is 25.5~, i.e. 58.8 - 33.3. (also by my other method, finding initial velocity at A, then substituting into S = 0.5 (u+v) t)

So my question is, with the +/- answer, is there a way of saying 25.5 is the correct answer mathematically?

Normally it is easy to distinguish a correct answer mathematically in these sort of equations, as one is positive and one is negative, but due to both answers being positive it has confused me...

I know by using the other method I get a correct answer, but I'm just curious as to how I can't use another seemingly valid technique and mathematically state one result is correct.

Anywho, any help much appreciated. :smile:

This is rather a tricky little question for M1, IMHO. As stated, the other solution isn't impossible.

If you use on the whole interval, then you get .

If u is positive, then the mass is going directly from A to C, and this takes the shorter time.

If u is negative then initially the mass is travelling away from C, comes to a stand still (due to the +ve acceleration), and then starts travelling towards C, passing through A again (this time with velocity ) and this takes the longer time.

So the question has some ambiguity, although there may be something in the exact wording of the question that allows you to distinguish between the two solutions.

From the English usage, I would assume it's going directly to C, but I wouldn't say the other solution is wrong.

The information about B is redundant.

Reply 3

JackF

OP

The original question:

A car is travelling along a straight horizontal road with constant acceleration. The car passes over three consecutive points A, B, C. AB = 100m, BC = 300m. The speed at B is 14m/s, the speed at C is 20m/s.
Find: a) The acceleration. b) the time taken for the car to travel from A to C.

EDIT:

I think I understand now why the two solutions exist, as from my other method I ignored the solution -8*(sqrt[2]). The -11.3 = u solution is the one which causes the longer time as you say.

So, ultimately, two things:

a) By looking at the 58.8 +/- 33.3 solution, I should be able to say the smaller solution is correct assuming 'u' is positive?
b) Am I right in saying the question has some ambiguity in the fact it does not state if 'u' is positive or negative? or am I overlooking some obvious statement in the question?

Reply 4

ghostwalker

17

JackF

...

Got to go out in about 10 seconds, so will reply when I'm back in a couple of hours, if no one else has.

Reply 5

ghostwalker

17

JackF

The original question:

A car is travelling along a straight horizontal road with constant acceleration. The car passes over three consecutive points A, B, C. AB = 100m, BC = 300m. The speed at B is 14m/s, the speed at C is 20m/s.
Find: a) The acceleration. b) the time taken for the car to travel from A to C.

a) By looking at the 58.8 +/- 33.3 solution, I should be able to say the smaller solution is correct assuming 'u' is positive?

You can say that, but it's almost impossible to spot, particularly if you've not worked out the initial velocity to start with. So I'd go with your former method.

b) Am I right in saying the question has some ambiguity in the fact it does not state if 'u' is positive or negative? or am I overlooking some obvious statement in the question?

The ambuity is eliminated by the statement "passes over three consecutive points A, B, C."

If the initial velocity was negative, it would have gone A, A, B, C. And equally common sense of what the car can do would eliminate this option as well. Additionally it would have had to have been decelerating initially rather than accelerating (although a lot of these words are open to interpretation, it's fairly clear what they are aiming at I think).

Hope that helped.

Reply 6

JackF

OP

Much help, exactly what I wanted to know, thank you, you've got my rep for the day.

Issue solved - end of thread.

M1 kinematics question

Related discussions

Latest

Trending

Trending

Articles for you