Standard +0.3 This is a straightforward kinematics problem using velocity-time graphs. It requires basic application of SUVAT equations and understanding that area under v-t graph equals displacement. All parts involve routine calculations with clearly stated information and no problem-solving insight needed—slightly easier than average A-level.
\includegraphics{figure_6}
The diagram shows the \((t, v)\) graph for the motion of a hoist used to deliver materials to different levels at a building site. The hoist moves vertically. The graph consists of straight line segments. In the first stage the hoist travels upwards from ground level for \(25\) s, coming to rest \(8\) m above ground level.
Find the greatest speed reached by the hoist during this stage. [2]
The second stage consists of a \(40\) s wait at the level reached during the first stage. In the third stage the hoist continues upwards until it comes to rest \(40\) m above ground level, arriving \(135\) s after leaving ground level. The hoist accelerates at \(0.02\) m s\(^{-2}\) for the first \(40\) s of the third stage, reaching a speed of \(V\) m s\(^{-1}\). Find
the value of \(V\), [3]
the length of time during the third stage for which the hoist is moving at constant speed, [4]
the deceleration of the hoist in the final part of the third stage. [3]
Particles P and Q, of masses m kg and 0.05 kg respectively, are attached to the ends of a light inextensible
string which passes over a smooth pulley. Q is attached to a particle R of mass 0.45 kg by a light inextensible
string. The strings are taut, and the portions of the strings not in contact with the pulley are vertical. P is in
contact with a horizontal surface when the particles are released from rest (see diagram). The tension in the
string QR is 2.52 N during the descent of R.
(i) (a) Find the acceleration of R during its descent. [2]
(b) By considering the motion of Q, calculate the tension in the string PQ during the descent of R. [3]
(ii) Find the value of m. [3]
R strikes the surface 0.5 s after release and does not rebound. During their subsequent motion, P does not
reach the pulley and Q does not reach the surface.
(iii) Calculate the greatest height of P above the surface. [8]
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\includegraphics{figure_6}
The diagram shows the $(t, v)$ graph for the motion of a hoist used to deliver materials to different levels at a building site. The hoist moves vertically. The graph consists of straight line segments. In the first stage the hoist travels upwards from ground level for $25$ s, coming to rest $8$ m above ground level.
\begin{enumerate}[label=(\roman*)]
\item Find the greatest speed reached by the hoist during this stage. [2]
\end{enumerate}
The second stage consists of a $40$ s wait at the level reached during the first stage. In the third stage the hoist continues upwards until it comes to rest $40$ m above ground level, arriving $135$ s after leaving ground level. The hoist accelerates at $0.02$ m s$^{-2}$ for the first $40$ s of the third stage, reaching a speed of $V$ m s$^{-1}$. Find
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item the value of $V$, [3]
\item the length of time during the third stage for which the hoist is moving at constant speed, [4]
\item the deceleration of the hoist in the final part of the third stage. [3]
\end{enumerate}
\hfill \mbox{\textit{OCR M1 Q6 [12]}}