OCR MEI M1 — Question 3 8 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Marks8
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TopicVectors Introduction & 2D
TypeVelocity from acceleration and initial conditions
DifficultyModerate -0.8 This is a straightforward kinematics question using constant acceleration formulas in vector form. Students need to apply v = u + at and s = ut + ½at² with given initial conditions, then calculate magnitude. It requires only direct application of standard M1 formulas with no problem-solving insight or geometric complications.
Spec1.10a Vectors in 2D: i,j notation and column vectors3.02e Two-dimensional constant acceleration: with vectors
In this question, the unit vectors \(\begin{pmatrix} 1 \\ 0 \end{pmatrix}\) and \(\begin{pmatrix} 0 \\ 1 \end{pmatrix}\) are in the directions east and north. Distance is measured in metres and time, \(t\), in seconds. A radio-controlled toy car moves on a flat horizontal surface. A child is standing at the origin and controlling the car. When \(t = 0\), the displacement of the car from the origin is \(\begin{pmatrix} 0 \\ -2 \end{pmatrix}\) m, and the car has velocity \(\begin{pmatrix} 2 \\ 0 \end{pmatrix}\) ms\(^{-1}\). The acceleration of the car is constant and is \(\begin{pmatrix} -1 \\ 1 \end{pmatrix}\) ms\(^{-2}\).
  1. Find the velocity of the car at time \(t\) and its speed when \(t = 8\). [4]
  2. Find the distance of the car from the child when \(t = 8\). [4]
Question 3:
AnswerMarks Guidance
3(i) vuat
2 1 2t
Velocity v t  (  )
0  1   t 
6
When t = 8, v 
 8 
AnswerMarks
speed (6)2 82 =10 m s-1M1
A1
A1
A1
AnswerMarks
[4]May be implied by either of the next two answers but not the final
answer. Evidence of use of vectors in question necessary.
May be implied by the final answer
Cao but condone no units
Give SC2 for 10 without working
AnswerMarks
(ii)rr ut 1at2
0 2
 0  2 1
r  8 1 82
2 0 2  1 
16
r 
 30 
AnswerMarks
Distance = 34 mM1
A1
A1
A1
AnswerMarks
[4]Use of correct equation with substitution. Condone omission of r
0
Or equivalent equation
Condone omission of r . Follow through for their value of v
0
Cao but may be implied by a correct final answer.
16 16
Allow for 35.77... fromr  and 37.57... fromr 
 32   34 
Question 3:
3 | (i) | vuat
2 1 2t
Velocity v t  (  )
0  1   t 
6
When t = 8, v 
 8 
speed (6)2 82 =10 m s-1 | M1
A1
A1
A1
[4] | May be implied by either of the next two answers but not the final
answer. Evidence of use of vectors in question necessary.
May be implied by the final answer
Cao but condone no units
Give SC2 for 10 without working
(ii) | rr ut 1at2
0 2
 0  2 1
r  8 1 82
2 0 2  1 
16
r 
 30 
Distance = 34 m | M1
A1
A1
A1
[4] | Use of correct equation with substitution. Condone omission of r
0
Or equivalent equation
Condone omission of r . Follow through for their value of v
0
Cao but may be implied by a correct final answer.
16 16
Allow for 35.77... fromr  and 37.57... fromr 
 32   34 
In this question, the unit vectors $\begin{pmatrix} 1 \\ 0 \end{pmatrix}$ and $\begin{pmatrix} 0 \\ 1 \end{pmatrix}$ are in the directions east and north.

Distance is measured in metres and time, $t$, in seconds.

A radio-controlled toy car moves on a flat horizontal surface. A child is standing at the origin and controlling the car.

When $t = 0$, the displacement of the car from the origin is $\begin{pmatrix} 0 \\ -2 \end{pmatrix}$ m, and the car has velocity $\begin{pmatrix} 2 \\ 0 \end{pmatrix}$ ms$^{-1}$.

The acceleration of the car is constant and is $\begin{pmatrix} -1 \\ 1 \end{pmatrix}$ ms$^{-2}$.

\begin{enumerate}[label=(\roman*)]
\item Find the velocity of the car at time $t$ and its speed when $t = 8$. [4]
\item Find the distance of the car from the child when $t = 8$. [4]
\end{enumerate}

\hfill \mbox{\textit{OCR MEI M1  Q3 [8]}}
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