Questions M1 (1912 questions)

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OCR MEI M1 2007 June Q7
Moderate -0.3
7 Fig. 7 is a sketch of part of the velocity-time graph for the motion of an insect walking in a straight line. Its velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), at time \(t\) seconds for the time interval \(- 3 \leqslant t \leqslant 5\) is given by $$v = t ^ { 2 } - 2 t - 8 .$$ \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3be85526-3872-42ac-8278-1d4a3cf75ff7-5_646_898_552_587} \captionsetup{labelformat=empty} \caption{Fig. 7}
\end{figure}
  1. Write down the velocity of the insect when \(t = 0\).
  2. Show that the insect is instantaneously at rest when \(t = - 2\) and when \(t = 4\).
  3. Determine the velocity of the insect when its acceleration is zero. Write down the coordinates of the point A shown in Fig. 7.
  4. Calculate the distance travelled by the insect from \(t = 1\) to \(t = 4\).
  5. Write down the distance travelled by the insect in the time interval \(- 2 \leqslant t \leqslant 4\).
  6. How far does the insect walk in the time interval \(1 \leqslant t \leqslant 5\) ?
OCR MEI M1 2007 June Q8
Moderate -0.3
8 A ball is kicked from ground level over horizontal ground. It leaves the ground at a speed of \(25 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and at an angle \(\theta\) to the horizontal such that \(\cos \theta = 0.96\) and \(\sin \theta = 0.28\).
  1. Show that the height, \(y \mathrm {~m}\), of the ball above the ground \(t\) seconds after projection is given by \(y = 7 t - 4.9 t ^ { 2 }\). Show also that the horizontal distance, \(x \mathrm {~m}\), travelled by this time is given by \(x = 24 t\).
  2. Calculate the maximum height reached by the ball.
  3. Calculate the times at which the ball is at half its maximum height. Find the horizontal distance travelled by the ball between these times.
  4. Determine the following when \(t = 1.25\).
    (A) The vertical component of the velocity of the ball.
    (B) Whether the ball is rising or falling. (You should give a reason for your answer.)
    (C) The speed of the ball.
  5. Show that the equation of the trajectory of the ball is $$y = \frac { 0.7 x } { 576 } ( 240 - 7 x )$$ Hence, or otherwise, find the range of the ball.
OCR MEI M1 2008 June Q1
Moderate -0.8
1 Fig. 1.1 shows a circular cylinder of mass 100 kg being raised by a light, inextensible vertical wire AB . There is negligible air resistance. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-2_310_261_488_941} \captionsetup{labelformat=empty} \caption{Fig. 1.1}
\end{figure}
  1. Calculate the acceleration of the cylinder when the tension in the wire is 1000 N .
  2. Calculate the tension in the wire when the cylinder has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). The cylinder is now raised inside a fixed smooth vertical tube that prevents horizontal motion but provides negligible resistance to the upward motion of the cylinder. When the wire is inclined at \(30 ^ { \circ }\) to the vertical, as shown in Fig. 1.2, the cylinder again has an upward acceleration of \(0.8 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-2_305_490_1354_829} \captionsetup{labelformat=empty} \caption{Fig. 1.2}
    \end{figure}
  3. Calculate the new tension in the wire.
OCR MEI M1 2008 June Q2
Easy -1.2
2 A particle has a position vector \(\mathbf { r }\), where \(\mathbf { r } = 4 \mathbf { i } - 5 \mathbf { j }\) and \(\mathbf { i }\) and \(\mathbf { j }\) are unit vectors in the directions east and north respectively.
  1. Sketch \(\mathbf { r }\) on a diagram showing \(\mathbf { i }\) and \(\mathbf { j }\) and the origin O .
  2. Calculate the magnitude of \(\mathbf { r }\) and its direction as a bearing.
  3. Write down the vector that has the same direction as \(\mathbf { r }\) and three times its magnitude.
OCR MEI M1 2008 June Q3
Moderate -0.8
3 An object of mass 5 kg has a constant acceleration of \(\binom { - 1 } { 2 } \mathrm {~m} \mathrm {~s} ^ { - 2 }\) for \(0 \leqslant t \leqslant 4\), where \(t\) is the time in seconds.
  1. Calculate the force acting on the object. When \(t = 0\), the object has position vector \(\binom { - 2 } { 3 } \mathrm {~m}\) and velocity \(\binom { 4 } { 5 } \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  2. Find the position vector of the object when \(t = 4\).
OCR MEI M1 2008 June Q4
Moderate -0.3
4 \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-3_346_981_781_584} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure} Particles P and Q move in the same straight line. Particle P starts from rest and has a constant acceleration towards Q of \(0.5 \mathrm {~m} \mathrm {~s} ^ { - 2 }\). Particle Q starts 125 m from P at the same time and has a constant speed of \(10 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) away from P . The initial values are shown in Fig. 4.
  1. Write down expressions for the distances travelled by P and by Q at time \(t\) seconds after the start of the motion.
  2. How much time does it take for P to catch up with Q and how far does P travel in this time?
OCR MEI M1 2008 June Q5
Moderate -0.3
5 Boxes A and B slide on a smooth, horizontal plane. Box A has a mass of 4 kg and box B a mass of 5 kg . They are connected by a light, inextensible, horizontal wire. Horizontal forces of 9 N and 135 N act on A and B in the directions shown in Fig. 5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-3_91_913_1959_616} \captionsetup{labelformat=empty} \caption{Fig. 5}
\end{figure} Calculate the tension in the wire joining the boxes.
OCR MEI M1 2008 June Q6
Moderate -0.8
6 In this question take \(\boldsymbol { g } = \mathbf { 1 0 }\).
A golf ball is hit from ground level over horizontal ground. The initial velocity of the ball is \(40 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) to the horizontal, where \(\sin \alpha = 0.6\) and \(\cos \alpha = 0.8\). Air resistance may be neglected.
  1. Find an expression for the height of the ball above the ground \(t\) seconds after projection.
  2. Calculate the horizontal range of the ball. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{170edb27-324e-44df-8dc1-7d8fbad680fe-4_358_447_360_849} \captionsetup{labelformat=empty} \caption{Fig. 7.1}
    \end{figure} A box of mass 8 kg is supported by a continuous light string ACB that is fixed at A and at B and passes through a smooth ring on the box at C, as shown in Fig. 7.1. The box is in equilibrium and the tension in the string section AC is 60 N .
OCR MEI M1 2008 June Q8
Moderate -0.3
8 The displacement, \(x \mathrm {~m}\), from the origin O of a particle on the \(x\)-axis is given by $$x = 10 + 36 t + 3 t ^ { 2 } - 2 t ^ { 3 }$$ where \(t\) is the time in seconds and \(- 4 \leqslant t \leqslant 6\).
  1. Write down the displacement of the particle when \(t = 0\).
  2. Find an expression in terms of \(t\) for the velocity, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of the particle.
  3. Find an expression in terms of \(t\) for the acceleration of the particle.
  4. Find the maximum value of \(v\) in the interval \(- 4 \leqslant t \leqslant 6\).
  5. Show that \(v = 0\) only when \(t = - 2\) and when \(t = 3\). Find the values of \(x\) at these times.
  6. Calculate the distance travelled by the particle from \(t = 0\) to \(t = 4\).
  7. Determine how many times the particle passes through O in the interval \(- 4 \leqslant t \leqslant 6\).
OCR MEI M1 2009 June Q1
Easy -1.2
1 The velocity-time graph shown in Fig. 1 represents the straight line motion of a toy car. All the lines on the graph are straight. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-2_579_1317_443_413} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure} The car starts at the point A at \(t = 0\) and in the next 8 seconds moves to a point B .
  1. Find the distance from A to B .
    \(T\) seconds after leaving A, the car is at a point C which is a distance of 10 m from B .
  2. Find the value of \(T\).
  3. Find the displacement from A to C .
OCR MEI M1 2009 June Q2
Moderate -0.8
2 A small box has weight \(\mathbf { W } \mathrm { N }\) and is held in equilibrium by two strings with tensions \(\mathbf { T } _ { 1 } \mathrm {~N}\) and \(\mathbf { T } _ { 2 } \mathrm {~N}\). This situation is shown in Fig. 2 which also shows the standard unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) that are horizontal and vertically upwards, respectively. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-2_259_629_1795_758} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} The tension \(\mathbf { T } _ { 1 }\) is \(10 \mathbf { i } + 24 \mathbf { j }\).
  1. Calculate the magnitude of \(\mathbf { T } _ { 1 }\) and the angle between \(\mathbf { T } _ { 1 }\) and the vertical. The magnitude of the weight is \(w \mathrm {~N}\).
  2. Write down the vector \(\mathbf { W }\) in terms of \(w\) and \(\mathbf { j }\). The tension \(\mathbf { T } _ { 2 }\) is \(k \mathbf { i } + 10 \mathbf { j }\), where \(k\) is a scalar.
  3. Find the values of \(k\) and of \(w\).
OCR MEI M1 2009 June Q3
Moderate -0.8
3 Fig. 3 is a sketch of the velocity-time graph modelling the velocity of a sprinter at the start of a race. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-3_588_1091_351_529} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. How can you tell from the sketch that the acceleration is not modelled as being constant for \(0 \leqslant t \leqslant 4\) ? The velocity of the sprinter, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), for the time interval \(0 \leqslant t \leqslant 4\) is modelled by the expression $$v = 3 t - \frac { 3 } { 8 } t ^ { 2 }$$
  2. Find the acceleration that the model predicts for \(t = 4\) and comment on what this suggests about the running of the sprinter.
  3. Calculate the distance run by the sprinter from \(t = 1\) to \(t = 4\).
OCR MEI M1 2009 June Q4
Standard +0.3
4 Fig. 4 shows a particle projected over horizontal ground from a point O at ground level. The particle initially has a speed of \(32 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) to the horizontal. The particle is a horizontal distance of 44.8 m from O after 5 seconds. Air resistance should be neglected. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-4_570_757_447_694} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. Write down an expression, in terms of \(\alpha\) and \(t\), for the horizontal distance of the particle from O at time \(t\) seconds after it is projected.
  2. Show that \(\cos \alpha = 0.28\).
  3. Calculate the greatest height reached by the particle.
OCR MEI M1 2009 June Q5
Moderate -0.8
5 The position vector of a toy boat of mass 1.5 kg is modelled as \(\mathbf { r } = ( 2 + t ) \mathbf { i } + \left( 3 t - t ^ { 2 } \right) \mathbf { j }\) where lengths are in metres, \(t\) is the time in seconds, \(\mathbf { i }\) and \(\mathbf { j }\) are horizontal, perpendicular unit vectors and the origin is O .
  1. Find the velocity of the boat when \(t = 4\).
  2. Find the acceleration of the boat and the horizontal force acting on the boat.
  3. Find the cartesian equation of the path of the boat referred to \(x\) - and \(y\)-axes in the directions of \(\mathbf { i }\) and \(\mathbf { j }\), respectively, with origin O . You are not required to simplify your answer. Section B (36 marks)
OCR MEI M1 2009 June Q6
Moderate -0.3
6 An empty open box of mass 4 kg is on a plane that is inclined at \(25 ^ { \circ }\) to the horizontal.
In one model the plane is taken to be smooth.
The box is held in equilibrium by a string with tension \(T \mathrm {~N}\) parallel to the plane, as shown in Fig. 6.1. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-5_314_575_621_785} \captionsetup{labelformat=empty} \caption{Fig. 6.1}
\end{figure}
  1. Calculate \(T\). A rock of mass \(m \mathrm {~kg}\) is now put in the box. The system is in equilibrium when the tension in the string, still parallel to the plane, is 50 N .
  2. Find \(m\). In a refined model the plane is rough.
    The empty box, of mass 4 kg , is in equilibrium when a frictional force of 20 N acts down the plane and the string has a tension of \(P \mathrm {~N}\) inclined at \(15 ^ { \circ }\) to the plane, as shown in Fig. 6.2. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{d6e78f93-ac2c-4053-87e4-5e5537d6dc3d-5_369_561_1653_790} \captionsetup{labelformat=empty} \caption{Fig. 6.2}
    \end{figure}
  3. Draw a diagram showing all the forces acting on the box.
  4. Calculate \(P\).
  5. Calculate the normal reaction of the plane on the box.
OCR MEI M1 2014 June Q1
Easy -1.2
1 Fig. 1 shows the velocity-time graph of a cyclist travelling along a straight horizontal road between two sets of traffic lights. The velocity, \(v\), is measured in metres per second and the time, \(t\), in seconds. The distance travelled, \(s\) metres, is measured from when \(t = 0\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-2_732_1116_513_477} \captionsetup{labelformat=empty} \caption{Fig. 1}
\end{figure}
  1. Find the values of \(s\) when \(t = 4\) and when \(t = 18\).
  2. Sketch the graph of \(s\) against \(t\) for \(0 \leqslant t \leqslant 18\).
OCR MEI M1 2014 June Q2
Moderate -0.8
2 The unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) shown in Fig. 2 are in the horizontal and vertically upwards directions. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-2_132_145_1726_968} \captionsetup{labelformat=empty} \caption{Fig. 2}
\end{figure} Forces \(\mathbf { p }\) and \(\mathbf { q }\) are given, in newtons, by \(\mathbf { p } = 12 \mathbf { i } - 5 \mathbf { j }\) and \(\mathbf { q } = 16 \mathbf { i } + 1.5 \mathbf { j }\).
  1. Write down the force \(\mathbf { p } + \mathbf { q }\) and show that it is parallel to \(8 \mathbf { i } - \mathbf { j }\).
  2. Show that the force \(3 \mathbf { p } + 10 \mathbf { q }\) acts in the horizontal direction.
  3. A particle is in equilibrium under forces \(k \mathbf { p } , 3 \mathbf { q }\) and its weight \(\mathbf { w }\). Show that the value of \(k\) must be - 4 and find the mass of the particle.
OCR MEI M1 2014 June Q3
Moderate -0.3
3 Fig. 3 shows a smooth ball resting in a rack. The angle in the middle of the rack is \(90 ^ { \circ }\). The rack has one edge at angle \(\alpha\) to the horizontal. The weight of the ball is \(W \mathrm {~N}\). The reaction forces of the rack on the ball at the points of contact are \(R \mathrm {~N}\) and \(S \mathrm {~N}\). \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-3_314_460_484_813} \captionsetup{labelformat=empty} \caption{Fig. 3}
\end{figure}
  1. Draw a fully labelled triangle of forces to show the forces acting on the ball. Your diagram must indicate which angle is \(\alpha\).
  2. Find the values of \(R\) and \(S\) in terms of \(W\) and \(\alpha\).
  3. On the same axes draw sketches of \(R\) against \(\alpha\) and \(S\) against \(\alpha\) for \(0 ^ { \circ } \leqslant \alpha \leqslant 90 ^ { \circ }\). For what values of \(\alpha\) is \(R < S\) ?
OCR MEI M1 2014 June Q4
Moderate -0.3
4 Fig. 4 illustrates a situation in which a film is being made. A cannon is fired from the top of a vertical cliff towards a ship out at sea. The director wants the cannon ball to fall just short of the ship so that it appears to be a near-miss. There are actors on the ship so it is important that it is not hit by mistake. The cannon ball is fired from a height 75 m above the sea with an initial velocity of \(20 \mathrm {~ms} ^ { - 1 }\) at an angle of \(30 ^ { \circ }\) above the horizontal. The ship is 90 m from the bottom of the cliff. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63a2dc41-5e8b-4275-8653-ece5067c4306-3_337_1242_1717_406} \captionsetup{labelformat=empty} \caption{Fig. 4}
\end{figure}
  1. The director calculates where the cannon ball will hit the sea, using the standard projectile model and taking the value of \(g\) to be \(10 \mathrm {~ms} ^ { - 2 }\). Verify that according to this model the cannon ball is in the air for 5 seconds. Show that it hits the water less than 5 m from the ship.
  2. Without doing any further calculations state, with a brief reason, whether the cannon ball would be predicted to travel further from the cliff if the value of \(g\) were taken to be \(9.8 \mathrm {~ms} ^ { - 2 }\).
OCR MEI M1 2014 June Q5
Moderate -0.8
5 In a science fiction story a new type of spaceship travels to the moon. The journey takes place along a straight line. The spaceship starts from rest on the earth and arrives at the moon's surface with zero speed. Its speed, \(v\) kilometres per hour at time \(t\) hours after it has started, is given by $$v = 37500 \left( 4 t - t ^ { 2 } \right) .$$
  1. Show that the spaceship takes 4 hours to reach the moon.
  2. Find an expression for the distance the spaceship has travelled at time \(t\). Hence find the distance to the moon.
  3. Find the spaceship's greatest speed during the journey. Section B (36 marks)
OCR MEI M1 2014 June Q6
Moderate -0.5
6 In this question the origin is a point on the ground. The directions of the unit vectors \(\left( \begin{array} { l } 1 \\ 0 \\ 0 \end{array} \right) , \left( \begin{array} { l } 0 \\ 1 \\ 0 \end{array} \right)\) and \(\left( \begin{array} { l } 0 \\ 0 \\ 1 \end{array} \right)\) are
\includegraphics[max width=\textwidth, alt={}, center]{63a2dc41-5e8b-4275-8653-ece5067c4306-5_398_689_434_689} Alesha does a sky-dive on a day when there is no wind. The dive starts when she steps out of a moving helicopter. The dive ends when she lands gently on the ground.
  • During the dive Alesha can reduce the magnitude of her acceleration in the vertical direction by spreading her arms and increasing air resistance.
  • During the dive she can use a power unit strapped to her back to give herself an acceleration in a horizontal direction.
  • Alesha's mass, including her equipment, is 100 kg .
  • Initially, her position vector is \(\left( \begin{array} { r } - 75 \\ 90 \\ 750 \end{array} \right) \mathrm { m }\) and her velocity is \(\left( \begin{array} { r } - 5 \\ 0 \\ - 10 \end{array} \right) \mathrm { ms } ^ { - 1 }\).
    1. Calculate Alesha's initial speed, and the initial angle between her motion and the downward vertical.
At a certain time during the dive, forces of \(\left( \begin{array} { r } 0 \\ 0 \\ - 980 \end{array} \right) \mathrm { N } , \left( \begin{array} { r } 0 \\ 0 \\ 880 \end{array} \right) \mathrm { N }\) and \(\left( \begin{array} { r } 50 \\ - 20 \\ 0 \end{array} \right) \mathrm { N }\) are acting on Alesha.
  • Suggest how these forces could arise.
  • Find Alesha's acceleration at this time, giving your answer in vector form, and show that, correct to 3 significant figures, its magnitude is \(1.14 \mathrm {~ms} ^ { - 2 }\). One suggested model for Alesha's motion is that the forces on her are constant throughout the dive from when she leaves the helicopter until she reaches the ground.
  • Find expressions for her velocity and position vector at time \(t\) seconds after the start of the dive according to this model. Verify that when \(t = 30\) she is at the origin.
  • Explain why consideration of Alesha's landing velocity shows this model to be unrealistic.
    •
    OCR MEI M1 2015 June Q1
    Moderate -0.8
    1 Fig. 1 shows four forces acting at a point. The forces are in equilibrium. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{f87e062a-fdf2-45cf-8bc0-d05683b28e1a-2_401_645_397_719} \captionsetup{labelformat=empty} \caption{Fig. 1}
    \end{figure} Show that \(P = 14\). Find \(Q\), giving your answer correct to 3 significant figures.
    OCR MEI M1 2015 June Q2
    Standard +0.3
    2 Fig. 2 shows a 6 kg block on a smooth horizontal table. It is connected to blocks of mass 2 kg and 9 kg by two light strings which pass over smooth pulleys at the edges of the table. The parts of the strings attached to the 6 kg block are horizontal. \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{f87e062a-fdf2-45cf-8bc0-d05683b28e1a-2_344_1143_1352_443} \captionsetup{labelformat=empty} \caption{Fig. 2}
    \end{figure}
    1. Draw three separate diagrams showing all the forces acting on each of the blocks.
    2. Calculate the acceleration of the system and the tension in each string.
    OCR MEI M1 2015 June Q3
    Moderate -0.3
    3 The map of a large area of open land is marked in 1 km squares and a point near the middle of the area is defined to be the origin. The vectors \(\binom { 1 } { 0 }\) and \(\binom { 0 } { 1 }\) are in the directions east and north. At time \(t\) hours the position vectors of two hikers, Ashok and Kumar, are given by: $$\begin{array} { l l } \text { Ashok } & \mathbf { r } _ { \mathrm { A } } = \binom { - 2 } { 0 } + \binom { 8 } { 1 } t , \\ \text { Kumar } & \mathbf { r } _ { \mathrm { K } } = \binom { 7 t } { 10 - 4 t } . \end{array}$$
    1. Prove that the two hikers meet and give the coordinates of the point where this happens.
    2. Compare the speeds of the two hikers.
    OCR MEI M1 2015 June Q4
    Moderate -0.8
    4 Fig. 4 illustrates a straight horizontal road. A and B are points on the road which are 215 metres apart and M is the mid-point of AB . When a car passes A its speed is \(12 \mathrm {~ms} ^ { - 1 }\) in the direction AB . It then accelerates uniformly and when it reaches \(B\) its speed is \(31 \mathrm {~ms} ^ { - 1 }\). \begin{figure}[h]
    \includegraphics[alt={},max width=\textwidth]{f87e062a-fdf2-45cf-8bc0-d05683b28e1a-3_138_1152_1247_459} \captionsetup{labelformat=empty} \caption{Fig. 4}
    \end{figure}
    1. Find the car's acceleration.
    2. Find how long it takes the car to travel from A to B .
    3. Find how long it takes the car to travel from A to M .
    4. Explain briefly, in terms of the speed of the car, why the time taken to travel from A to M is more than half the time taken to travel from A to B .