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Edexcel M2 2016 June Q6
13 marks Standard +0.3
6. [In this question the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.] At \(t = 0\) a particle \(P\) is projected from a fixed point \(O\) with velocity ( \(7 \mathbf { i } + 7 \sqrt { 3 } \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\). The particle moves freely under gravity. The position vector of a point on the path of \(P\) is \(( x \mathbf { i } + y \mathbf { j } ) \mathrm { m }\) relative to \(O\).
  1. Show that $$y = \sqrt { 3 } x - \frac { g } { 98 } x ^ { 2 }$$
  2. Find the direction of motion of \(P\) when it passes through the point on the path where \(x = 20\) At time \(T\) seconds \(P\) passes through the point with position vector \(( 2 \lambda \mathbf { i } + \lambda \mathbf { j } ) \mathrm { m }\) where \(\lambda\) is a positive constant.
  3. Find the value of \(T\).
    DO NOT WIRITE IN THIS AREA
Edexcel M2 2016 June Q7
14 marks Standard +0.3
7. Two particles \(A\) and \(B\), of mass \(m\) and \(2 m\) respectively, are moving in the same direction along the same straight line on a smooth horizontal surface, with \(B\) in front of \(A\). Particle \(A\) has speed \(3 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and particle \(B\) has speed \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\). Particle \(A\) collides directly with particle \(B\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 2 } { 3 }\). The direction of motion of both particles is not changed by the collision. Immediately after the collision, \(A\) has speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\) and \(B\) has speed \(w \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Show that \(w = \frac { 23 } { 9 }\).
    2. Find the value of \(v\). When \(A\) and \(B\) collide they are 3 m from a smooth vertical wall which is perpendicular to their direction of motion. After the collision with \(A\), particle \(B\) hits the wall and rebounds. The coefficient of restitution between \(B\) and the wall is \(\frac { 1 } { 2 }\). There is a second collision between \(A\) and \(B\) at a point \(d \mathrm {~m}\) from the wall.
  2. Find the value of \(d\).
Edexcel M2 2017 June Q1
5 marks Moderate -0.8
  1. A particle of mass 4 kg is moving with velocity \(( 2 \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) when it receives an impulse of \(( 7 \mathbf { i } - 5 \mathbf { j } )\) Ns.
Find the speed of the particle immediately after receiving the impulse.
Edexcel M2 2017 June Q2
8 marks Standard +0.3
  1. A cyclist and his bicycle have a total mass of 75 kg . The cyclist is moving up a straight road inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 21 }\). The non-gravitational resistance to motion is modelled as a constant force of magnitude \(R\) newtons. The cyclist is working at a constant rate of 280 W and moving at a constant speed of \(2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
    1. Find the value of \(R\).
    Later the cyclist cycles down the same road on the same bicycle. He is again working at a constant rate of 280 W and the resistance to motion is now modelled as a constant force of magnitude 60 N .
  2. Find the acceleration of the cyclist at the instant when his speed is \(3.5 \mathrm {~ms} ^ { - 1 }\).
Edexcel M2 2017 June Q3
9 marks Moderate -0.3
3. A particle \(P\) moves along the \(x\)-axis. At time \(t = 0 , P\) passes through the origin with speed \(6 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) in the positive \(x\) direction. The acceleration of \(P\) at time \(t\) seconds, where \(t \geqslant 0\), is \(( 4 t - 8 ) \mathrm { m } \mathrm { s } ^ { - 2 }\) in the positive \(x\) direction.
    1. Show that \(P\) is instantaneously at rest when \(t = 1\)
    2. Find the other value of \(t\) for which \(P\) is instantaneously at rest.
  2. Find the total distance travelled by \(P\) in the interval \(1 \leqslant t \leqslant 4\)
Edexcel M2 2017 June Q4
11 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-12_609_639_296_657} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform rod \(A B\) has mass 5 kg and length 4 m . The rod is held in a horizontal position by a light inextensible string. The end \(A\) of the rod rests against a rough vertical wall. One end of the string is attached to the rod at \(B\) and the other end is attached to the wall at a point \(D\). The point \(D\) is vertically above \(A\), with \(A D = 3 \mathrm {~m}\). A particle of mass 2 kg is attached to the rod at \(C\), where \(A C = 0.5 \mathrm {~m}\), as shown in Figure 1. The rod is in equilibrium in a vertical plane perpendicular to the wall. The coefficient of friction between the rod and the wall is \(\mu\). Find
  1. the tension in the string,
  2. the magnitude of the force exerted by the wall on the rod at \(A\),
  3. the range of possible values of \(\mu\).
Edexcel M2 2017 June Q5
13 marks Standard +0.3
5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-16_255_1242_301_360} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} A smooth straight ramp is fixed to horizontal ground. The ramp has length 8 m and is inclined at \(30 ^ { \circ }\) to the ground, as shown in Figure 2. A particle \(P\) of mass 0.7 kg is projected from a point \(A\) at the bottom of the ramp, up a line of greatest slope of the ramp, with speed \(u \mathrm {~m} \mathrm {~s} ^ { - 1 }\). As \(P\) reaches the point \(B\) at the top of the ramp, \(P\) has speed \(4.2 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
  1. By considering energy, find the value of \(u\). After leaving the ramp at \(B\), the particle \(P\) moves freely under gravity until it hits the ground at a point \(C\). Immediately before hitting the ground at \(C\), particle \(P\) is moving at \(\theta ^ { \circ }\) below the horizontal with speed \(w \mathrm {~ms} ^ { - 1 }\). Find
    1. the value of \(w\),
    2. the value of \(\theta\),
  3. the horizontal distance from \(B\) to \(C\).
Edexcel M2 2017 June Q6
13 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{266c4f52-f35f-459c-9184-836b0f3baf5b-20_570_608_287_669} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} The uniform lamina \(A B C D\) is a square with sides of length \(6 a\). The point \(E\) is the midpoint of side \(A D\). The triangle \(C D E\) is removed from the square to form the uniform lamina \(L\), shown in Figure 3. The centre of mass of \(L\) is at the point \(G\).
  1. Show that the distance of \(G\) from the side \(A B\) is \(\frac { 7 } { 3 } a\).
  2. Find the distance of \(G\) from the side \(A E\). The mass of \(L\) is \(M\). A particle of mass \(k M\) is attached to \(L\) at the point \(E\). The lamina, with the particle attached, is freely suspended from \(A\) and hangs in equilibrium with the diagonal \(A C\) vertical.
  3. Find the value of \(k\).
Edexcel M2 2017 June Q7
16 marks Standard +0.3
7. Three particles \(A , B\) and \(C\) lie at rest in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). The particles \(A\), \(B\) and \(C\) have mass \(6 m\), 4 \(m\) and \(m\) respectively. Particle \(A\) is projected towards \(B\) with speed \(3 u\) and \(A\) collides directly with \(B\). Immediately after this collision, the speed of \(B\) is \(w\). The coefficient of restitution between \(A\) and \(B\) is \(\frac { 1 } { 6 }\).
  1. Show that \(w = \frac { 21 } { 10 } u\).
  2. Express the total kinetic energy of \(A\) and \(B\) lost in the collision as a fraction of the total kinetic energy of \(A\) and \(B\) immediately before the collision. After being struck by \(A\), the particle \(B\) collides directly with \(C\). The coefficient of restitution between \(B\) and \(C\) is \(e\). After the collision between \(B\) and \(C\), there are no further collisions between the particles.
  3. Find the range of possible values of \(e\).
Edexcel M2 2018 June Q1
6 marks Moderate -0.8
  1. A particle \(P\) of mass 0.7 kg is moving with velocity ( \(\mathbf { i } - 2 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\) when it receives an impulse. Immediately after receiving the impulse, \(P\) is moving with velocity \(( 3 \mathbf { i } + 4 \mathbf { j } ) \mathrm { m } \mathrm { s } ^ { - 1 }\).
    1. Find the impulse.
    2. Find, in degrees, the size of the angle between the direction of the impulse and the direction of motion of \(P\) immediately before receiving the impulse.
      (3)
Edexcel M2 2018 June Q2
9 marks Standard +0.3
2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a3f28425-4acf-4878-b0e3-15b5bc8a92d7-04_494_1116_226_415} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform rod \(A B\), of mass 6 kg and length 1.6 m , rests with its end \(A\) on rough horizontal ground. The rod is held in equilibrium at \(30 ^ { \circ }\) to the horizontal by a light string attached to the rod at \(B\). The string is at \(40 ^ { \circ }\) to the horizontal and lies in the same vertical plane as the rod, as shown in Figure 1. The tension in the string is \(T\) newtons. The coefficient of friction between the ground and the rod is \(\mu\).
  1. Show that, to 3 significant figures, \(T = 27.1\)
  2. Find the set of values of \(\mu\) for which equilibrium is possible. \includegraphics[max width=\textwidth, alt={}, center]{a3f28425-4acf-4878-b0e3-15b5bc8a92d7-07_27_40_2802_1893}
Edexcel M2 2018 June Q3
8 marks Standard +0.3
3. A cyclist and his bicycle, with a combined mass of 75 kg , move along a straight horizontal road. The cyclist is working at a constant rate of 180 W . There is a constant resistance to the motion of the cyclist and his bicycle of magnitude \(R\) newtons. At the instant when the speed of the cyclist is \(4 \mathrm {~m} \mathrm {~s} ^ { - 1 }\), his acceleration is \(0.2 \mathrm {~m} \mathrm {~s} ^ { - 2 }\).
  1. Find the value of \(R\). Later, the cyclist moves up a straight road with a constant speed \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The road is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 21 }\). The cyclist is working at a rate of 180 W and the resistance to the motion of the cyclist and his bicycle from non-gravitational forces is again the same constant force of magnitude \(R\) newtons.
  2. Find the value of \(v\).
Edexcel M2 2018 June Q4
12 marks Standard +0.3
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a3f28425-4acf-4878-b0e3-15b5bc8a92d7-12_702_1182_226_379} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The uniform lamina \(A B C\) is an isosceles triangle with \(A B = B C , A C = 6 a\) and the distance from \(B\) to \(A C\) is \(3 a\). The uniform lamina \(M N C\) is an isosceles triangle with \(M N = N C\) and \(M C = 3 a\). Triangles \(A B C\) and \(M N C\) are similar and are made of the same material. The lamina \(L\) is formed by fixing triangle \(M N C\) on top of triangle \(A B C\), as shown in Figure 2.
  1. Show that the distance of the centre of mass of \(L\) from \(A C\) is \(\frac { 9 } { 10 } a\) The lamina \(L\) is freely suspended from \(B\) and hangs in equilibrium.
  2. Find, to the nearest degree, the size of the angle between \(A B\) and the downward vertical.
Edexcel M2 2018 June Q5
12 marks Standard +0.3
5. A particle \(P\) of mass 0.3 kg moves under the action of a single force \(\mathbf { F }\) newtons. At time \(t\) seconds \(( t \geqslant 0 ) , P\) has velocity \(\mathbf { v } \mathrm { m } \mathrm { s } ^ { - 1 }\), where $$\mathbf { v } = \left( 3 t ^ { 2 } - 4 t \right) \mathbf { i } + \left( 3 t ^ { 2 } - 8 t + 4 \right) \mathbf { j }$$
  1. Find \(\mathbf { F }\) when \(t = 4\) At the instants when \(P\) is at the points \(A\) and \(B\), particle \(P\) is moving parallel to the vector i.
  2. Find the distance \(A B\).
Edexcel M2 2018 June Q6
14 marks Standard +0.3
6. A particle \(P\) is projected from a fixed point \(A\) with speed \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\alpha\) above the horizontal and moves freely under gravity. As \(P\) passes through the point \(B\) on its path, \(P\) is moving with speed \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) at an angle \(\beta\) below the horizontal.
  1. By considering energy, find the vertical distance between \(A\) and \(B\). Particle \(P\) takes 1.5 seconds to travel from \(A\) to \(B\).
  2. Find the size of angle \(\alpha\).
  3. Find the size of angle \(\beta\).
  4. Find the length of time for which the speed of \(P\) is less than \(8 \mathrm {~m} \mathrm {~s} ^ { - 1 }\).
Edexcel M2 2018 June Q7
14 marks Standard +0.8
7. Three particles \(A\), \(B\) and \(C\) have masses \(2 m , 3 m\) and \(4 m\) respectively. The particles lie at rest in a straight line on a smooth horizontal surface, with \(B\) between \(A\) and \(C\). Particle \(A\) is projected towards \(B\) with speed \(u\) and collides directly with \(B\). The coefficient of restitution between \(A\) and \(B\) is \(e\). The kinetic energy of \(A\) immediately after the collision is one ninth of the kinetic energy of \(A\) immediately before the collision. Given that the direction of motion of \(A\) is unchanged by the collision,
  1. find the value of \(e\). After the collision between \(A\) and \(B\) there is a direct collision between \(B\) and \(C\). The coefficient of restitution between \(B\) and \(C\) is \(f\), where \(f < \frac { 3 } { 4 }\). The speed of \(B\) immediately after the collision with \(C\) is \(V\).
    1. Express \(V\) in terms of \(f\) and \(u\).
    2. Hence show that there will be a second collision between \(A\) and \(B\).
Edexcel M2 2020 June Q1
5 marks Moderate -0.3
  1. A particle of mass 2 kg is moving with velocity \(( 5 \mathbf { i } + 3 \mathbf { j } ) \mathrm { ms } ^ { - 1 }\) when it receives an impulse \(\mathbf { I N }\) s, such that \(\mathbf { I } = a \mathbf { i } + b \mathbf { j }\)
Immediately after receiving the impulse, the particle is moving with velocity \(\lambda ( \mathbf { i } + \mathbf { j } ) \mathrm { ms } ^ { - 1 }\), where \(\lambda\) is a constant. Given that the magnitude of \(\mathbf { I }\) is \(\sqrt { 40 }\), find the two possible impulses.
(5)
Edexcel M2 2020 June Q2
9 marks Standard +0.3
  1. A truck of weight 9000 N is travelling up a hill on a straight road that is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 15 }\)
When the truck travels up the hill with the engine working at \(3 P\) watts, the truck is moving at a constant speed of \(12 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) Later on, the truck travels down the hill along the same road, with the engine working at \(P\) watts. At the instant when the speed of the truck is \(12 \mathrm {~ms} ^ { - 1 }\), the acceleration of the truck is \(\frac { g } { 20 }\) The resistance to motion of the truck from non-gravitational forces is a constant force of magnitude \(R\) newtons in all circumstances. Find (i) the value of \(P\),
(ii) the value of \(R\).
WIHW SIHI NIT INHM ION OC
WIIV SIHI NI III IM I ON OC
VAYV SIHI NI JLIUM ION OO
Edexcel M2 2020 June Q3
9 marks Standard +0.8
3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-08_476_725_251_605} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} A uniform rod \(A B\), of mass 25 kg and length 3 m , has end \(A\) resting on rough horizontal ground. The end \(B\) rests against a rough vertical wall. The rod is in a vertical plane perpendicular to the wall.
The coefficient of friction between the rod and the ground is \(\frac { 4 } { 5 }\) The coefficient of friction between the rod and the wall is \(\frac { 3 } { 5 }\) The rod rests in limiting equilibrium.
The rod is at an angle of \(\theta\) to the ground, as shown in Figure 1. Find the exact value of \(\tan \theta\).
DO NOT WRITEIN THIS AREA
VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO
Edexcel M2 2020 June Q4
9 marks Standard +0.8
4. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-12_662_716_255_614} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} The uniform lamina \(L\), shown shaded in Figure 2, is formed by removing the square \(P Q R V\), of side \(2 a\), and the square \(R S T U\), of side \(4 a\), from a uniform square lamina \(A B C D\), of side \(8 a\). The lines \(Q R U\) and \(V R S\) are straight. The side \(A D\) is parallel to \(P V\) and the side \(A B\) is parallel to \(P Q\). The distance between \(A D\) and \(P V\) is \(a\) and the distance between \(A B\) and \(P Q\) is \(a\). The centre of mass of \(L\) is at the point \(G\).
  1. Show that the distance of \(G\) from the side \(A D\) is \(\frac { 42 } { 11 } a\) The mass of \(L\) is \(M\). A particle of mass \(k M\) is attached to \(L\) at \(C\). The lamina, with the attached particle, is freely suspended from \(B\) and hangs in equilibrium with \(B C\) making an angle of \(45 ^ { \circ }\) with the horizontal.
  2. Find the value of \(k\).
    VIXV SIHIANI III IM IONOOVIAV SIHI NI JYHAM ION OOVI4V SIHI NI JLIYM ION OO
Edexcel M2 2020 June Q5
10 marks Moderate -0.3
5. At time \(t\) seconds ( \(t \geqslant 0\) ), a particle \(P\) has velocity \(\mathbf { v m ~ s } ^ { - 1 }\), where $$\mathbf { v } = \left( 3 t ^ { 2 } - 9 t + 6 \right) \mathbf { i } + \left( t ^ { 2 } + t - 6 \right) \mathbf { j }$$
  1. Find the acceleration of \(P\) when \(t = 3\) When \(t = 0 , P\) is at the fixed point \(O\).
    The particle comes to instantaneous rest at the point \(A\).
  2. Find the distance \(O A\).
Edexcel M2 2020 June Q6
10 marks Standard +0.3
6. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-20_273_1058_246_443} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} A rough straight ramp is fixed to horizontal ground. The ramp has length 15 m and is inclined at an angle \(\alpha\) to the ground, where \(\tan \alpha = \frac { 5 } { 12 }\). The line \(A B\) is a line of greatest slope of the ramp, where \(A\) is at the bottom of the ramp, and \(B\) is at the top of the ramp, as shown in Figure 3. A particle \(P\) of mass 6 kg is projected up the ramp with speed \(14 \mathrm {~m} \mathrm {~s} ^ { - 1 }\) from \(A\) in a straight line towards \(B\). The coefficient of friction between \(P\) and the ramp is 0.25
  1. Find the work done against friction as \(P\) moves from \(A\) to \(B\). At the instant \(P\) reaches \(B\), the speed of \(P\) is \(v \mathrm {~ms} ^ { - 1 }\). After leaving the ramp at \(B\), the particle \(P\) moves freely under gravity until it hits the horizontal ground at the point \(C\). Immediately before hitting the ground at \(C\), the speed of \(P\) is \(w \mathrm {~ms} ^ { - 1 }\)
  2. Use the work-energy principle to find
    1. the value of \(v\),
    2. the value of \(w\).
      \includegraphics[max width=\textwidth, alt={}, center]{1dea68fe-7916-41ed-894e-6b48f8d989bb-23_86_49_2617_1884}
Edexcel M2 2020 June Q7
10 marks Standard +0.3
7. Particle \(A\) of mass \(3 m\) is moving in a straight line with speed \(2 u\) on a smooth horizontal surface. Particle \(A\) collides directly with particle \(B\) of mass \(m\), which is moving along the same straight line and in the same direction as \(A\). Immediately before the collision, the speed of \(B\) is \(u\).
As a result of the collision, the direction of motion of \(B\) is unchanged and the kinetic energy gained by \(B\) is \(\frac { 48 } { 25 } m u ^ { 2 }\)
  1. Find the coefficient of restitution between \(A\) and \(B\).
    (8) After the collision, \(B\) hits a smooth fixed vertical wall that is perpendicular to the direction of motion of \(B\). The coefficient of restitution between \(B\) and the wall is \(f\). Given that the speed of \(B\) immediately after first hitting the wall is equal to the speed of \(A\) immediately after its first collision with \(B\),
  2. find the value of \(f\).
Edexcel M2 2020 June Q8
13 marks Standard +0.8
8. [In this question, the unit vectors \(\mathbf { i }\) and \(\mathbf { j }\) are in a vertical plane, with \(\mathbf { i }\) being horizontal and \(\mathbf { j }\) being vertically upwards.] \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1dea68fe-7916-41ed-894e-6b48f8d989bb-28_426_1145_347_338} \captionsetup{labelformat=empty} \caption{Figure 4}
\end{figure} At time \(t = 0\), a small ball is projected from a fixed point \(O\) on horizontal ground. The ball is projected from \(O\) with velocity ( \(p \mathbf { i } + q \mathbf { j }\) ) \(\mathrm { ms } ^ { - 1 }\), where \(p\) and \(q\) are positive constants. The ball moves freely under gravity. At time \(t = 3\) seconds, the ball passes through the point \(A\) with velocity ( \(8 \mathbf { i } - 12 \mathbf { j }\) ) \(\mathrm { m } \mathrm { s } ^ { - 1 }\), as shown in Figure 4.
  1. Find the speed of the ball at the instant it is projected from \(O\). For an interval of \(T\) seconds the speed, \(v \mathrm {~m} \mathrm {~s} ^ { - 1 }\), of the ball is such that \(v \leqslant 10\)
  2. Find the value of \(T\). At the point \(B\) on the path of the ball, the direction of motion of the ball is perpendicular to the direction of motion of the ball at \(A\).
  3. Find the vertical height of \(B\) above \(A\).
Edexcel M2 2021 June Q1
5 marks Moderate -0.3
  1. A motorcyclist and his motorcycle have a combined mass of 480 kg .
The motorcyclist drives down a straight road that is inclined at an angle \(\theta\) to the horizontal, where \(\sin \theta = \frac { 1 } { 12 }\), with the engine of the motorcycle working at 3.5 kW . The motorcycle is moving at a constant speed of \(V \mathrm {~m} \mathrm {~s} ^ { - 1 }\). The resistance to the motion of the motorcycle is modelled as a constant force with magnitude 20 V newtons. Find the value of \(V\).
(5)