Standard +0.2 This is a standard M2 multi-part question covering routine mechanics topics (forces, kinematics, power, vectors). Parts 1-3 require straightforward application of standard formulas (F=ma, KE=½mv², P=Fv). Part 4 involves basic vector calculus. The lamina equilibrium problem is more involved but still follows standard centre of mass methods. Overall slightly easier than average due to being mostly procedural with clear solution paths.
A car of mass 1200 kg decelerates from \(30 \mathrm {~ms} ^ { - 1 }\) to \(20 \mathrm {~ms} ^ { - 1 }\) in 6 seconds at a constant rate.
Find the magnitude, in N , of the decelerating force.
Find the loss, in J , in the car's kinetic energy.
A particle moves in a straight line from \(A\) to \(B\) in 5 seconds. At time \(t\) seconds after leaving \(A\), the velocity of the particle is \(\left( 32 t - 3 t ^ { 2 } \right) \mathrm { ms } ^ { - 1 }\).
Calculate the straight-line distance \(A B\).
Find the acceleration of the particle when \(t = 3\).
Eddie, whose mass is 71 kg , rides a bicycle of mass 25 kg up a hill inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 12 }\). When Eddie is working at a rate of 600 W , he is moving at a constant speed of \(6 \mathrm {~ms} ^ { - 1 }\).
Find the magnitude of the non-gravitational resistance to his motion.
A boat leaves the point \(O\) and moves such that, \(t\) seconds later, its position vector relative to \(O\) is \(\left( t ^ { 2 } - 2 \right) \mathbf { i } + 2 t \mathbf { j }\), where the vectors \(\mathbf { i }\) and \(\mathbf { j }\) both have magnitude 1 metre and are directed parallel and perpendicular to the shoreline through \(O\).
Find the speed with which the boat leaves \(O\).
Show that the boat has constant acceleration and state the magnitude of this acceleration.
Find the value of \(t\) when the boat is 40 m from \(O\).
Comment on the limitations of the given model of the boat's motion.
The diagram shows a body which may be modelled as a uniform lamina.
The body is suspended from the point marked \(A\) and rests in equilibrium.
Calculate, to the nearest degree, the angle which the edge \(A B\) then makes with the vertical.
(8 marks)
Frank suggests that the angle between \(A B\) and the vertical would be smaller if the lamina were made from lighter material.
State, with a brief explanation, whether Frank is correct.
(2 marks)
\section*{MECHANICS 2 (A) TEST PAPER 1 Page 2}
\begin{enumerate}
\item A car of mass 1200 kg decelerates from $30 \mathrm {~ms} ^ { - 1 }$ to $20 \mathrm {~ms} ^ { - 1 }$ in 6 seconds at a constant rate.\\
(a) Find the magnitude, in N , of the decelerating force.\\
(b) Find the loss, in J , in the car's kinetic energy.
\item A particle moves in a straight line from $A$ to $B$ in 5 seconds. At time $t$ seconds after leaving $A$, the velocity of the particle is $\left( 32 t - 3 t ^ { 2 } \right) \mathrm { ms } ^ { - 1 }$.\\
(a) Calculate the straight-line distance $A B$.\\
(b) Find the acceleration of the particle when $t = 3$.
\item Eddie, whose mass is 71 kg , rides a bicycle of mass 25 kg up a hill inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 12 }$. When Eddie is working at a rate of 600 W , he is moving at a constant speed of $6 \mathrm {~ms} ^ { - 1 }$.\\
Find the magnitude of the non-gravitational resistance to his motion.
\item A boat leaves the point $O$ and moves such that, $t$ seconds later, its position vector relative to $O$ is $\left( t ^ { 2 } - 2 \right) \mathbf { i } + 2 t \mathbf { j }$, where the vectors $\mathbf { i }$ and $\mathbf { j }$ both have magnitude 1 metre and are directed parallel and perpendicular to the shoreline through $O$.\\
(a) Find the speed with which the boat leaves $O$.\\
(b) Show that the boat has constant acceleration and state the magnitude of this acceleration.\\
(c) Find the value of $t$ when the boat is 40 m from $O$.\\
(d) Comment on the limitations of the given model of the boat's motion.
\item
\end{enumerate}
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\includegraphics[max width=\textwidth, alt={}]{996976f3-2a97-4c68-8c97-f15a3bfde9a2-1_446_595_1965_349}
\end{center}
The diagram shows a body which may be modelled as a uniform lamina.
The body is suspended from the point marked $A$ and rests in equilibrium.\\
(a) Calculate, to the nearest degree, the angle which the edge $A B$ then makes with the vertical.\\
(8 marks)
Frank suggests that the angle between $A B$ and the vertical would be smaller if the lamina were made from lighter material.\\
(b) State, with a brief explanation, whether Frank is correct.\\
(2 marks)
\section*{MECHANICS 2 (A) TEST PAPER 1 Page 2}
\hfill \mbox{\textit{Edexcel M2 Q1 [4]}}