OCR MEI M1 2006 January — Question 5 6 marks

Exam BoardOCR MEI
ModuleM1 (Mechanics 1)
Year2006
SessionJanuary
Marks6
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicVariable acceleration (vectors)
TypeFind velocity by integrating acceleration
DifficultyModerate -0.3 This is a straightforward vector mechanics question requiring direct substitution into given formulae, application of F=ma, and integration of acceleration to find velocity with one constant to determine. All steps are routine M1 techniques with no problem-solving insight needed, making it slightly easier than average.
Spec3.02g Two-dimensional variable acceleration3.03d Newton's second law: 2D vectors

5 The acceleration of a particle of mass 4 kg is given by \(\mathbf { a } = ( 9 \mathbf { i } - 4 t \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }\), where \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors and \(t\) is the time in seconds.
  1. Find the acceleration of the particle when \(t = 0\) and also when \(t = 3\).
  2. Calculate the force acting on the particle when \(t = 3\). The particle has velocity \(( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\) when \(t = 1\).
  3. Find an expression for the velocity of the particle at time \(t\).

5 The acceleration of a particle of mass 4 kg is given by $\mathbf { a } = ( 9 \mathbf { i } - 4 t \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 2 }$, where $\mathbf { i }$ and $\mathbf { j }$ are unit vectors and $t$ is the time in seconds.\\
(i) Find the acceleration of the particle when $t = 0$ and also when $t = 3$.\\
(ii) Calculate the force acting on the particle when $t = 3$.

The particle has velocity $( 4 \mathbf { i } + 2 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }$ when $t = 1$.\\
(iii) Find an expression for the velocity of the particle at time $t$.

\hfill \mbox{\textit{OCR MEI M1 2006 Q5 [6]}}