Edexcel M2 2023 January — Question 1 8 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Year2023
SessionJanuary
Marks8
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Mark schemeDownload PDF ↗
TopicPower and driving force
TypeFind acceleration on incline given power
DifficultyStandard +0.3 This is a standard M2 power-speed-acceleration question requiring P=Fv and F=ma with two straightforward applications. Part (a) involves horizontal motion with one equation setup, part (b) adds an incline component but follows the same method. Slightly above average due to the two-part structure and inclusion of inclined plane, but uses routine techniques with no novel insight required.
Spec3.03d Newton's second law: 2D vectors6.02l Power and velocity: P = Fv6.02m Variable force power: using scalar product
  1. A truck of mass 1500 kg is moving on a straight horizontal road.
The engine of the truck is working at a constant rate of 30 kW .
The resistance to the motion of the truck is modelled as a constant force of magnitude \(R\) newtons.
At the instant when the truck is moving at a speed of \(20 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the acceleration of the truck is \(0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
  1. Find the value of \(R\). Later on, the truck is moving up a straight road that is inclined at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = \frac { 1 } { 8 }\) The resistance to the motion of the truck from non-gravitational forces is modelled as a constant force of magnitude 500 N .
    The engine of the truck is again working at a constant rate of 30 kW . At the instant when the speed of the truck is \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\), the deceleration of the truck is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\)
  2. Find the value of \(V\)
\begin{enumerate}
  \item A truck of mass 1500 kg is moving on a straight horizontal road.
\end{enumerate}

The engine of the truck is working at a constant rate of 30 kW .\\
The resistance to the motion of the truck is modelled as a constant force of magnitude $R$ newtons.\\
At the instant when the truck is moving at a speed of $20 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the acceleration of the truck is $0.6 \mathrm {~m} \mathrm {~s} ^ { - 2 }$\\
(a) Find the value of $R$.

Later on, the truck is moving up a straight road that is inclined at an angle $\alpha$ to the horizontal, where $\sin \alpha = \frac { 1 } { 8 }$

The resistance to the motion of the truck from non-gravitational forces is modelled as a constant force of magnitude 500 N .\\
The engine of the truck is again working at a constant rate of 30 kW . At the instant when the speed of the truck is $V \mathrm {~m} \mathrm {~s} ^ { - 1 }$, the deceleration of the truck is $0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }$\\
(b) Find the value of $V$

\hfill \mbox{\textit{Edexcel M2 2023 Q1 [8]}}
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