Constant deceleration

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Christian Lawson-Perfect	said	Ready to use	8 years, 8 months ago
Amy Chadwick	said	Needs to be tested	8 years, 10 months ago

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Christian Lawson-Perfect 8 years, 8 months ago

Gave some feedback: Ready to use

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Christian Lawson-Perfect 8 years, 8 months ago

Saved a checkpoint:

Moved part d (time taken) up to part b, so students aren't tempted to apply the resistance force, and added adaptive marking to replace $v$ with the answer to part a.

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Christian Lawson-Perfect commented 8 years, 10 months ago

Statement: you decelerate at a rate, not a speed.
a)
I would say "after it has travelled ...", just to make things clearer.
b)
I think you mean "tension" instead of "thrust".
c)
This part is trivial - just subtract the given resistance from your answer to b. What's the point of it? It's not used in the following part, and in fact students might think they need to recalculate the acceleration for the new force.
d)
I'd use $s = ut + \frac{1}{2}at^2$ instead of reusing the speed I worked out in part a, to avoid a rounding error. Maybe mention both methods in the advice, and allow wiggle room in the marking to tolerate any rounding error.

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Amy Chadwick 8 years, 10 months ago

Gave some feedback: Needs to be tested

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Amy Chadwick 8 years, 10 months ago

Created this.

Name	Status	Author	Last Modified
Constant deceleration	Ready to use	Amy Chadwick	24/08/2016 11:39
John's copy of Constant deceleration	draft	John Bridges	18/09/2016 23:44
Simon's copy of Constant deceleration	draft	Simon Thomas	29/04/2019 09:31

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Question statement

A caravan of mass $\var{mass} \ \mathrm{kg}$ is pulled on a rope by a car along a straight horizontal road. It decelerates at a constant rate of $\var{-a} \ \mathrm{ms^{-2}}$ from an initial speed of $\var{u} \ \mathrm{ms^{-1}}$ . There is no resistance to motion.

Give your answers to each of the following questions to 3 decimal places.

Give any introductory information the student needs.

			Name	Type	Generated Value

mass	integer	362
a	number	-3.25
u	number	30
s	integer	28
v	number	26.796
resistance	integer	23

Automatically regenerate variables?

Name

Data type

Value

A random number between and (inclusive) with step size

Description

Describe what this variable represents, and list any assumptions made about its value.

Can an exam override the value of this variable?

Generated value: `integer`

362

This variable doesn't seem to be used anywhere.

Advice

a)

We are told that the caravan is decelerating at a rate of $a= \var{a} \ \mathrm{ms^{-2}}$ . We know $u=\var{u}$ and $s=\var{s}$ and we want $v$ , therefore we can use the equation $v^2=u^2+2as$ .

$\begin{align} v^2 & = u^2 + 2as \\ & = \var{u}^2 + \left( 2 \times \var{a} \times \var{s} \right) \\ & = \var{u^2 + 2*a*s} \end{align}$

Therefore $v = \sqrt{\var{u^2 + 2*a*s}} = \var{v}$ . So the speed is $\var{v} \ \mathrm{ms^{-1}}$ .

b)

Having worked out the speed $v$ of the caravan after it has travelled $\var{s} \, \mathrm{m}$ , we can use the formula $v = u + at$ to find the time taken.

$\begin{align} v &= u + at \\ t &= \frac{v-u}{a} \\ &= \simplify[!basic]{({v}-{u})/{a}} \\ &= \var{precround((v-u)/a,3)} \end{align}$

The caravan takes $\var{precround((v-u)/a,3)} \, \mathrm{s}$ to travel $\var{s} \, \mathrm{m}$ .

c)

To find the tension, $T$ in Newtons, we resolve in the direction of acceleration, where $a=\var{a}$ and $T$ is acting in the opposite direction.

$\begin{align} F & = ma \\ - T & = \var{mass} \times \var{a} \\ T & = \var{precround(mass*-a,3)}. \end{align}$

The tension in the rope is $\var{precround(mass*-a,3)} \ \mathrm{N}$ .

d)

If the caravan experiences a resistance to motion of magnitude $\var{resistance}N$ this resistance will act in the opposite direction to acceleration.

$\begin{align} F & = ma \\ - T - \var{resistance} & = \var{mass} \times \var{a}\\ T & = \left(\var{mass} \times \var{-a}\right) - \var{resistance} \\ & = \var{precround(mass*-a - resistance,3)}. \end{align}$

The tension in the rope is $\var{precround(mass*-a-resistance,3)} \ \mathrm{N}$ .

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This question is used in the following exam:

Dynamics - Forces by Amy Chadwick in Maths Support Wiki - Mechanics.

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Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect commented 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Error in variable testing condition

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Generated value: `integer`

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Constant deceleration

Metadata

Taxonomy: mathcentre

Taxonomy: Kind of activity

Taxonomy: Context

Contributors

Feedback

History

Comment

Checkpoint description

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect 8 years, 8 months ago

Christian Lawson-Perfect commented 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Amy Chadwick 8 years, 10 months ago

Error in variable testing condition

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Warning

Generated value: integer

Parts

Number entry

Advanced settings

a)

b)

c)

d)

Generated value: `integer`