| Exam Board | OCR MEI |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2011 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | SUVAT simultaneous equations: find u and a |
| Difficulty | Moderate -0.3 This is a straightforward SUVAT problem requiring students to set up and solve simultaneous equations from given information (s=8, t=32, v=2.25). While it involves two unknowns (u and a), the algebraic manipulation is routine and the problem type is standard textbook fare for M1, making it slightly easier than average. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Either for \(u\) first: \(8 = \frac{1}{2}(u + 2.25) \times 32\) | M1 | Using \(s = \frac{1}{2}(u + v)t\) |
| \(u = -1.75\) so \(1.75 \text{ m s}^{-1}\) | A1 | |
| \(2.25 = -1.75 + 32a\) | M1 | Use of any appropriate suvat with their values and correct signs |
| \(a = 0.125\) so \(0.125 \text{ m s}^{-2}\) | F1 | Sign must be consistent with their \(u\), FT from their value of \(u\) |
| Directions of \(u\) and \(a\) are defined | F1 | Establish directions of both \(u\) and \(a\) in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks. |
| 5 | ||
| Or for \(a\) first: \(8 = 2.25 \times 32 - \frac{1}{2} \times a \times 32^2\) | M1 | Using \(s = vt - \frac{1}{2}at^2\) |
| \(a = 0.125\) so \(0.125 \text{ m s}^{-2}\) | A1 | |
| \(2.25 = u + 32 \times 0.125\) | M1 | Use of any appropriate suvat with their values and correct signs |
| \(u = -1.75\) so \(1.75 \text{ m s}^{-1}\) | F1 | Sign must be consistent with their \(a\), FT from their value of \(a\) |
| Directions of \(u\) and \(a\) are defined | F1 | Establish directions of both \(u\) and \(a\) in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks. |
| 5 |
| Answer | Marks | Guidance |
|---|---|---|
| Set up one relevant equation with \(a\) and \(u\) | M1 | Using one of \(v = u + at\), \(s = ut + \frac{1}{2}at^2\) and \(v^2 = u^2 + 2as\) |
| Set up second relevant equation with \(a\) and \(u\) | M1 | Using another of \(v = u + at\), \(s = ut + \frac{1}{2}at^2\) and \(v^2 = u^2 + 2as\) |
| Solving to find \(u = -1.75\) so \(1.75 \text{ m s}^{-1}\) | A1 | |
| Solving to find \(a = 0.125\) so \(0.125 \text{ m s}^{-2}\) | F1 | FT from their value of \(u\) or \(a\), whichever found first |
| Directions of \(u\) and \(a\) are defined | F1 | Establish directions of both \(u\) and \(a\) in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks. |
| 5 |
**Either** for $u$ first: $8 = \frac{1}{2}(u + 2.25) \times 32$ | M1 | Using $s = \frac{1}{2}(u + v)t$
$u = -1.75$ so $1.75 \text{ m s}^{-1}$ | A1 |
$2.25 = -1.75 + 32a$ | M1 | Use of any appropriate suvat with their values and correct signs
$a = 0.125$ so $0.125 \text{ m s}^{-2}$ | F1 | Sign must be consistent with their $u$, FT from their value of $u$
Directions of $u$ and $a$ are defined | F1 | Establish directions of both $u$ and $a$ in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks.
| | 5 |
**Or** for $a$ first: $8 = 2.25 \times 32 - \frac{1}{2} \times a \times 32^2$ | M1 | Using $s = vt - \frac{1}{2}at^2$
$a = 0.125$ so $0.125 \text{ m s}^{-2}$ | A1 |
$2.25 = u + 32 \times 0.125$ | M1 | Use of any appropriate suvat with their values and correct signs
$u = -1.75$ so $1.75 \text{ m s}^{-1}$ | F1 | Sign must be consistent with their $a$, FT from their value of $a$
Directions of $u$ and $a$ are defined | F1 | Establish directions of both $u$ and $a$ in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks.
| | 5 |
**Or using simultaneous equations**
Set up one relevant equation with $a$ and $u$ | M1 | Using one of $v = u + at$, $s = ut + \frac{1}{2}at^2$ and $v^2 = u^2 + 2as$
Set up second relevant equation with $a$ and $u$ | M1 | Using another of $v = u + at$, $s = ut + \frac{1}{2}at^2$ and $v^2 = u^2 + 2as$
Solving to find $u = -1.75$ so $1.75 \text{ m s}^{-1}$ | A1 |
Solving to find $a = 0.125$ so $0.125 \text{ m s}^{-2}$ | F1 | FT from their value of $u$ or $a$, whichever found first
Directions of $u$ and $a$ are defined | F1 | Establish directions of both $u$ and $a$ in terms of A and B. May be shown by a diagram, eg showing A and B and a line between them together with an arrow to show the positive direction. Without a diagram, the wording must be absolutely clear: eg do not accept left/right, forwards/backwards without a diagram or more explanation. Dependent on both M marks.
| | 5 |
---2 A particle travels with constant acceleration along a straight line. A and B are points on this line 8 m apart.
The motion of the particle is as follows.
\begin{itemize}
\item Initially it is at A.
\item After 32 s it is at B .
\item When it is at B its speed is $2.25 \mathrm {~m} \mathrm {~s} ^ { - 1 }$ and it is moving away from A .
\end{itemize}
In either order, calculate the acceleration and the initial velocity of the particle, making the directions clear.
\hfill \mbox{\textit{OCR MEI M1 2011 Q2 [5]}}